Probability

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Probabilityby Total Gadha - Sunday, 8 November 2009, 10:31 PM

Dagny and I are big Harry Potter fans. I still read the books while eating or going tobed. At night when Dagny is screaming at me to turn off the lights and go to sleep, Ihave a sudden impulse to swish my ‘imaginary’ wand in air and yell ‘IMPEDIMENTA!’ Ahwell, it is not advisable to throw spells at your wife, especially the one who is equallygood at them, if you care about your marital bliss. So I resist the temptation. But thestranglehold of imagination is not lost on me. And imagination and dream building forma sizeable portion of our psyche if we are to get ahead in life. They also fuel our desireto focus and work hard towards our goals. I still remember that the only thing thatpropelled me hard towards cracking IIT JEE was that I wanted to win the heart of a girlin my school. I would dream about million fanciful situations in which she was looking atme wide-eyed with admiration after JEE results were announced. Alas, the dream didpush me to my coveted institute but did not gave the courage to open my mouth infront of her. Even during our CAT preparations, Dagny and I both shared the common

dream- that of staying together in IIM and traveling the world after passing out. Although I cracked CAT- twice- we realized that ourdream was impossible while serving someone else. And then glory of an MBA fizzled out. We have let go of IIMs but we still cling on

hard to our dream. Wish we have Floo powder or a Portkey.

This is a month when you should be stoking your dreams, trying to imagine what kind of life you want to lead, which places you want togo to, where do you want to live, what kind of home do you want, which girl do you want to propose to, etc… Take good care of yourdreams. They will give you your lust for life, your raison de etre, your enthusiasm for CAT, and your killer instinct. If you want to really

go for it, start with finding your dreams.

This lesson goes to Ashwini, whose continuous entreaties (TG sir please write a lesson on probability) in our CAT CBT C lub forced me tosit up and finish the task. So if you want to say thanks for this lesson, say thanks to him. But yes, if you feel this lesson is useful to you,

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Re: Probabilityby AsHwIn Drmz - Sunday, 8 November 2009, 10:53 PM

So finally ....A lesson on Probability....

Thanks a lot Tg...

btw...m Ashwin not Ashwini ...

Ashwin

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Re: Probabilityby amit kheterpal - Sunday, 8 November 2009, 11:10 PM

thanks a lot tg sir and ashwin too.

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Re: Probabilityby wali khan - Sunday, 8 November 2009, 11:44 PM

thanks a lot TG

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Re: Probabilityby honey chaubey - Monday, 9 November 2009, 12:02 AM

Thanks Sir

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Re: Probabilityby harsh tulsiyan - Monday, 9 November 2009, 12:56 AM

thanks sir .. it he lped to clear many doubts ...

and thanks to ashwin..

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Re: Probabilityby steven hyde - Monday, 9 November 2009, 01:05 AM

Sir, One small doubt. In the beginning of this lesson when you mention the example of tossing 3 coins and say that that the possibleoutcomes are (HHH),....(TTT), isn't (HTH) equivalent to saying (THH) or (HHT) ? That is to say, are the 3 coins distinguishable? Isometimes take tossing 3 coins to be the same as tossing a coin thrice. Is there an error in this think ing?Thanks .Steven

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Re: Probabilityby KAMONASISH AAYUSH MAZUMDAR - Monday, 9 November 2009, 04:13 AM

thank you so much :D for listening to our request a lways and so many other little things that we can't really thank you for.

now officia l answers to PnC lesson plz

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Re: Probabilityby whirl wind - Monday, 9 November 2009, 06:57 AM

no steven,

When u take it as tossing 3 coins - u need to take care of which 2 coins are showing heads(or ta ils).(1st & 2nd coins or 2nd&3rd coins or3rd and 1st coins).

If u take it as tossing the same coin thrice, u consider it to be the throw in which u get the heads.(on the 1st&2nd throws, or 2nd &3rd or3rd&1st throws).

Nothing wrong in think ing tossing 3 coins to be the same as tossing the same coin thrice.

Whirlwind

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Re: Probabilityby shahnas ameer - Monday, 9 November 2009, 09:06 AM

thankzzzzzzzzzzz

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Re: Probabilityby Ronak kabani - Monday, 9 November 2009, 10:49 AM

Thnx TG

The probability of getting a sum correct on probability has definite ly increased.

Ronak

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Re: Probabilityby shank jos - Monday, 9 November 2009, 11:29 AM

Thanks TG

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Re: Probabilityby Soumyakanta Das - Monday, 9 November 2009, 01:13 PM

Thanks a Lot TG Sir and Ashwin...

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Re: Probabilityby divya kalkotwar - Monday, 9 November 2009, 01:48 PM

thanks a lot TG

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Re: Probabilityby ashraf laskar - Monday, 9 November 2009, 02:11 PM

thanks a lot TG Sir for such a beautiful article .......

the funda to solve probability using geometry is new to me....hope that now i can attempt probability questions with more confidence.......

-Ashraf

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Re: Probabilityby Vickram Asokan - Monday, 9 November 2009, 02:54 PM

Hi TG,

Good article at a great time.

Have a doubt in the problems solved after the article.

Second from last question, which says,

" A,B and C are two speakers among 7 diff speakers "

Isn't that three speakers ( A,B and C ). Another thing is that there are two possible arrangements that are favorable for our criteria ["A"speaking before "B"]. ( i.e ABC and ACB are favorable).

Please correct me if I am wrong. Thanks for the article...

-Vickram.

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Re: Probabilityby Priya Ranjan Dutta - Monday, 9 November 2009, 03:46 PM

Vickram,

Read the question carefully. A speaks before B who speaks before C.. only one case ABC.. ..

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Re: Probability



























by Neelesh Sethi - Monday, 9 November 2009, 08:10 PM

Thanx a lot sir..probability by geometry were outstanding..sir how u thought of that method..it was difficult to even imagine that geometrycan be used in probab..1 doubt ,If question is: if out of 6 speakers..find probability that abc speak after first speaker and in order, afollowed by b followed by c? then what will be the answer

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Re: Probabilityby suraj verma - Monday, 9 November 2009, 08:48 PM

superb TG sir...thanx a ton

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Re: Probabilityby rakesh salecha - Tuesday, 10 November 2009, 02:09 AM

thank you sir

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Re: Probabilityby Suvrodip Banerje - Tuesday, 10 November 2009, 04:20 AM

Hello,

Although am a keen reader of your articles,yet I have never posted any comment.But can't resist writing today,partly for the introductionpart and partly to point a very minor m istake(am sure it's a typo)..

In the question

In a match between two players A,B the chances of A winning are 3/5.If A and B play 5 matches in a succession,whta is the probabilitythat B wins at least 3 matches(assuming no draws)?

the solution should be:

5C3*(2/5)^3*(3/5)^2 + 5c4*(2/5)^4*(3/5) + 5c5*(2/5)^5.....

Dreamz Rule

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Re: Probabilityby Total Gadha - Tuesday, 10 November 2009, 10:55 AM

Hi Surodip,

Corrected the typo. Thanks for pointing it out.

Total Gadha

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Re: Probabilityby Rohit Ghosh - Tuesday, 10 November 2009, 11:57 AM

Hi,

How the total probability of drawing a red ball is "19/45"?

Please help

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Re: Probabilityby abhay agrawal - Tuesday, 10 November 2009, 12:43 PM

from time I've become a fan of your articles and always wait for the new one. I like one

thing most in your articles and that is your explanation by examples. Although in two

years of my preparation for CAT I never liked probability but after reading this article

I'm really feeling very comfortable in it. And one thing more that after reading this

article my probability in cracking CAT became higher.

So thanx to you and Ashwini for forcing you to write a wonderful article.Show parent | Reply

Re: Probabilityby Total Gadha - Tuesday, 10 November 2009, 01:06 PM


























Thanks Lazy

Fill the 'Tell a Friend' to help us if you can?

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Re: Probabilityby Pradip Roy - Wednesday, 11 November 2009, 10:21 AM

Hi TG

Thanks a lot for the article.

I have a doubt about the Square-Coin sum.... can u expla in that in a lil more detail (centre of the coin is 1 unit inside of the square, sohow did we get 8 units instead of 9 (10-1) units)

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Re: Probabilityby Rahul Arora - Wednesday, 11 November 2009, 11:05 AM

Hi Pradip,

As the original square is of 10 unit length, so the inner square side = 10 - 1(from left side) - 1 (from right side), thus, 8. Hope, it he lpsyou.

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Re: Probabilityby abhay agrawal - Wednesday, 11 November 2009, 12:22 PM

Hi TG sir, I have question

Q. There is a bag and in that bag there are two pockets. In one pocket of the bag

there are 2 gold coins & 3 silver coins and in another pocket there are 3 gold coins & 2

silver coins. If a man choose one of pocket of the bag and pick up one coin from that

pocket and place it in another pocket of the bag. Now he randomly pick up one coin from

this pocket in which he place the coin than what is probability of getting a silver coin.

plz give the answer with the explanationShow parent | Reply

Re: Probabilityby piyush ja in - Wednesday, 11 November 2009, 08:03 PM

well gr8 article with some wonderful probabilities m big fan of urs but just one thing i cant make it out in prob. having 3 speakers A,B,C among 7 and v require to calculate probability ofcases whr A speaks before B and B before C .

i tried it in this manner by fix ing C at 1 position say last and now calculate as in case of A speaks before B among 6 speakers,again fix Cat position 6 and calculate again same among 5 speakers sim ilarly till C sit at 3 position .so it comes out (360+60+12+3+1)/7!

so plz. expla in thispiyush ja in

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plz helpby Avishek Chakraborty - Wednesday, 11 November 2009, 10:11 PM

guys I have one problem

numbers 1 to 20(1,2,3,...20) are arranged. wat is the probabilty that 2 will appear before any other even number?

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Re: Probabilityby Total Gadha - Wednesday, 11 November 2009, 11:44 PM

Hi Lazy,

There are four cases here-

gold coin from Pocket 1 then silver coin from pocket 2- (2/5) ×(1/3)

silver coin from Pocket 1 then silver coin from pocket 2- (3/5) × (1/2)gold coin from Pocket 2 then silver coin from pocket 1- (3/5) × (1/2)silver coin from Pocket 1 then silver coin from pocket 1- (2/5) × (2/3)

Sum all these

Total Gadha





















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Re: Probabilityby Total Gadha - Wednesday, 11 November 2009, 11:50 PM

Hi Piyush,

You are calculating it wrong in your method. For example, when A is in second position, you are doing that rest of thelower seats can be arranged in 5! ways out of which B would come before C in half. Unfortunately, you are not taking

care of speaker no. 1 here whom you can select in 4C1 = 4 ways. So total number of ways are 4 × 60 = 240.

And so on. When A is in third place, you will have to select speaker no. 1 & 2 (not equal to B or C). Then you can dowhat you are doing.

Answer would be same by your method also. it would be 840/7!

Total Gadha

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problemby Avishek Chakraborty - Wednesday, 11 November 2009, 11:55 PM

TG Sir since u r here thought if I can get the answer of this problemnumbers 1 to 20(1,2,3,...20) are arranged. wat is the probabilty that 2will appear before any other even number?

thanks in advance

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Re: Probabilityby Avishek Chakraborty - Thursday, 12 November 2009, 12:26 AM

numbers 1 to 20(1,2,3,...20) are arranged. Wat is the probabilty that 2 will appear before any other even number?

I think the ans is 1/10.See there are 10 even numbers in total. now there will be equal number of arrangements in which one even number comes first. likenumbr of cases in which 2 comes b4 ne othr evn no=number of cases in which 4 comes b4 ne othr evn number=...=number of cases where20 comes b4 ne othr evn numberso the in this prob favourable cases=total cases/10=20!/10so probability = 1/10m I rite? can any1 confirm

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Re: Probabilityby abhay agrawal - Thursday, 12 November 2009, 10:56 AM

hello sir, I'm tak ing this problem a little bit different and getting the same ans what u got. but officia l ans is diff. my takeif I choose any pocket for pick ing the coin then there will be only 2 possibility that it will be Gold or Silver. nowconsider 1st pocketI place gold coin in it than the probability of getting silver = 1/2 x 3/6I place silver coin in it than 1/2 x 4/6now consider 2nd pocketI place gold coin than 1/2 x 2/6I place silver coin than 1/2 x 3/6Now sum all these and u will get the same ans. is my approach right?

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Re: Probabilityby Total Gadha - Thursday, 12 November 2009, 01:12 PM

Hi Lazy,

My answer is coming to be 1/2 (you will have to multiply all the terms in my answer by 1/2 for choosing the first bag)but yours is different. Will think about your approach later. Please tell me the offic ial answer for now.

Total Gadha

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Re: Probabilityby userdce . - Thursday, 12 November 2009, 06:34 PM

content is great as ever but seems font got a bit distorted in the pictures























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Re: Probabilityby piyush ja in - Thursday, 12 November 2009, 07:13 PM

ok i got it sir thank u very much and congrats for 3rd anniversary of TG.

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Re: Probabilityby abhay agrawal - Friday, 13 November 2009, 11:34 AM

yes sir, you r right. In my approach I was not considering the probability of pick ing a coin from any pocket. now i got my answer. thanx sir

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Re: Probabilityby ankhuri dubey - Friday, 13 November 2009, 08:34 PM

Inte lligent!!.. i have a question Sir...wts d probability that the 'sarah n nidhi' in one of the questions weren't just a coincidence..??..:P

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Re: Probabilityby Total Gadha - Friday, 13 November 2009, 08:56 PM

Ankhuri

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Re: Probabilityby Vickram Asokan - Monday, 16 November 2009, 12:42 PM

Hi Ms.Priya,

Thanks for the clarification. I now understand why I am getting more negations in MockCATs...

Thanks,-Vickram.

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Re: Probabilityby deepika gandhi - Monday, 16 November 2009, 02:27 PM

pls...can u giv few more tips on functions,graphs and inequalities

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Re: Probabilityby Pankaj Kumar - Thursday, 19 November 2009, 12:19 AM

Hi TG,

CAT is coming and by giving this article at this crucia l time, u helped many as probability with permutations and combinations is bitchallenging topic.I know I'm becoming demanding here , but a humble and last request for this CAT- please give some tips for Logarithms topic a lso

please..please please

I have immense appreciation for your great way helping manyTG will have to go much higher from here.., I encourage all people here to spread TG so that more n more people can benefit from it.

Many Thanks Again

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Re: Probabilityby Avishek Chakraborty - Thursday, 26 November 2009, 11:39 PM

guys,

7 distinct accidents occur in a week. what is the probability that they all occur on the same day of the week??

options are 1. (1/7)^7 2. (1/7)^6 3. (1/2)^7 4. 7/ 2^7

since since a single accident can occur on any single day so (1/7)^7 and for 7 days it becomes (1/7)^6. is itcorrect?

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Re: Probabilityby Abhijit Roy - Monday, 14 December 2009, 10:09 PM

From very first time i Logged in to this site ...I find it very helpful ...n dis is nt only in regard to preparing my se lf for cat but a lso for otherexam too.....

I was facing some problem wid probability ...n moreover being a non math student ..it was bit difficult for me to understand ......

So all thing is dat thank you very much for providing us such a useful n helpful site ......






























It's a request to u sir if u can post something on Permutation n combination ... and Logarithm ....

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Re: Probabilityby gaurav adlakha - Tuesday, 26 January 2010, 04:20 PM

great help.........

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Re: Probability doubtby vasu r - Monday, 25 October 2010, 10:52 PM

Paul the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited topredict ICC world cup matches in 2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each.Each team in a group plays the other teams in the group. The top two teams from each group enter the semi finals ( after which the winneris decided by knockout).

However, Paul has a soft spot for India and when India plays any team, Paul a lways backs India. Alas, his predictions on matchesinvolving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches.What is the probability that India will win the ICC world cup?

a) (2/3)^10 b) (2/3)^9 + 8/3 * (2/3)^9

c) 8/3 * (2/3)^9 d) (2/3)^10 + 8/3*(2/3)^9

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Re: Probability doubtby kushal ganatra - Saturday, 30 October 2010, 11:49 AM

i think answer should be D

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Re: Probability doubtby Pradeep Mavilla - Wednesday, 3 November 2010, 01:16 AM

Thanks for the article

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Re: Probabilityby aagesh sharma - Monday, 27 June 2011, 06:26 PM

applying 4 cbt is the irst thing i'm gonna do with this months salary

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Re: Probabilityby manisha dalan - Wednesday, 3 August 2011, 02:50 PM

In the question-what is the probability that the red ball came from bag1...

is the Probability of drawing a red ball from bag1 not 3/5 instead of 1/5..

please correct me if m wrong.

thanks TG,

manisha

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Re: Probabilityby ADITYA PATEL - Wednesday, 10 August 2011, 11:36 AM

Hello TG Sir,Thanks for writing such a nice article.I have 1 question.in the example you gave for mutually exclusive events,(in rolling 2 dices, the probability of getting sum 4 or sum 7), you considered boththe events as mutually exclusive, but i have a question why can't these events be considered as independent events and why can't we useprobability equation P(A) * P(B)? I know sir i am wrong but i am not able to get the exact difference between Mutually exclusive events andindependent events. P lease do reply sir.

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Re: Probabilityby ritu aggarwal - Thursday, 11 August 2011, 04:48 PM

sir..i have one ques of prob..

in poker, 5 cards are dealt to a person. assuming all C(52,5) are equallty like ly. what is the probability of be ing dealt

(i) one pair, (a,a,b,c,d) where a,b,c,d are distinct?(ii) two pairs (a,a,b,b,c) where a,b,c are distinct?



























i didnt understand this question sir.

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Re: Probabilityby destiny unruled - Friday, 12 August 2011, 01:05 PM

@ Aditya

Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring or

vice-versa.

Now, if on the two dices sum of numbers showing up is 4, then it can definitely not be 7 which means they are not

independent events.

On the other hand. two events are mutually exclusive if they can not occur at the same time, which is true in this

case.

So, getting a sum 4 and a sum 7 are mutually exclusive events.

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Re: Probabilityby In lonely planet i live - Wednesday, 8 August 2012, 08:28 AM

Well written article sir.

P lease help me finding the answer for the below question.

A man alternate ly tosses a coin and throws a die beginning with the coin. The probability that he gets a head in the coin before he gets a 5or 6 in the dice is?

Thanks in advance.

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Re: Probabilityby TG Team - Wednesday, 8 August 2012, 10:47 AM

It is simply sum of infinite GP: 1/2 + (1/2)(4/6)(1/2) + (1/2)(4/6)(1/2)(4/6)(1/2) + ... = 1/2 + (1/2)(1/3) + (1/2)(1/3)(1/3) + ... = 3/4.

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Re: Probabilityby Rhythm Goyal - Wednesday, 8 August 2012, 07:46 PM

Hi TG,

First of a ll, Thanks a ton for such an nice ly organised article. Often Probability confuse us and is a reason of dislike. Now we have a visionabout how to approach a problem.

I have 3 querries re lated to your artica l above and need your help for the same:

1) There is a question above as "10 persons are sitting around a round table. What is the probability that two particular persons are NOTsitting next to each other?"I fa iled to undestand how we got 2*8!/9! as the probability that 2 particular persons are sitting next to each other. Where did a ll this 8!, 9!and product by 2 came in?

2) There is a question in Inverse probability section as "Dagny's purse contains 4 coins which can be 1 rupee coins or 5 rupees coins. 2coins are drawn and are both foubnd to be 5 rupees coins. If the coins are replaced in the purse and Dandny draws out another coin, whatis the probability that it is a 1 rupee coin?"

As it was mentioned in the question itse lf that 2 coins of 5 are drawn, implied that a lteast there are 2 coins of 5 rupee each in thepurse.Thus there were 3 cases a) a ll 5 rupee coinb) 3 coins of 5 rupee and 1 coin of 1 rupeec) 2 coins of 5 rupee and 2 coins of 1 rupee

Now why probability of drawing 2 5rupees coins were obtained?also how come its 1, 1/2 and 1/6 respective ly for case a, b,and c.should it not be 1/3, 1/4, 1/6 respective ly.

Further, I didnt understand how we have calculated the probablilty of case a, b & c.

3) In a question as "If we throw a dice 10 times what is the probability of it showing 6 exactly 3 times?"Should not the solution be (1/6)^3 * (5/6)^7.Why was it needed to found "ways of those 3 out of 10" i.e 10c3 and getting its product

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Re: Probabilityby Rhythm Goyal - Tuesday, 14 August 2012, 08:55 PM

Hi Kamal Sir,


















First of a ll, Thanks a ton for such an nice ly organised article. Often Probability confuse us and is a reason of dislike. Now we have a visionabout how to approach a problem.

I have 3 querries re lated to your artica l above and need your help for the same:

1) There is a question above as "10 persons are sitting around a round table. What is the probability that two particular persons are NOTsitting next to each other?"I fa iled to undestand how we got 2*8!/9! as the probability that 2 particular persons are sitting next to each other. Where did a ll this 8!, 9!and product by 2 came in?

2) There is a question in Inverse probability section as "Dagny's purse contains 4 coins which can be 1 rupee coins or 5 rupees coins. 2coins are drawn and are both foubnd to be 5 rupees coins. If the coins are replaced in the purse and Dandny draws out another coin, whatis the probability that it is a 1 rupee coin?"

As it was mentioned in the question itse lf that 2 coins of 5 are drawn, implied that a lteast there are 2 coins of 5 rupee each in thepurse.Thus there were 3 cases a) a ll 5 rupee coinb) 3 coins of 5 rupee and 1 coin of 1 rupeec) 2 coins of 5 rupee and 2 coins of 1 rupee

Now why probability of drawing 2 5rupees coins were obtained?also how come its 1, 1/2 and 1/6 respective ly for case a, b,and c.should it not be 1/3, 1/4, 1/6 respective ly.

Further, I didnt understand how we have calculated the probablilty of case a, b & c.

3) In a question as "If we throw a dice 10 times what is the probability of it showing 6 exactly 3 times?"Should not the solution be (1/6)^3 * (5/6)^7.Why was it needed to found "ways of those 3 out of 10" i.e 10c3 and getting its product

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Re: Probabilityby Harsh Aggarwal - Tuesday, 28 August 2012, 08:42 PM

Hi ,Approach :- I fee l by keeping 2 at first place and arranging the rest of 9 even numbers in any order will give the required answer.

Favourable case is 2 at first place.So no. of favourable case is 9! for keeping 2 at first place .

And total case is 10 ! for 10 even numbers.

Prob = 9!/ 10 ! = 1/10 .

Hence your answer is correct.

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Re: Probabilityby DHEERAJ KUMAR - Thursday, 30 August 2012, 06:54 PM

Hi Rythm lets see what happens in case a)the probability that the first coin drawn is 4/4 =1and the probability that the second coin is a lso a 5 rupee coin is 3/3=1 ....therefore , the probability that in two draws it is a 5 rupee coin is 1*1=1.

b)for this case the probability of getting 5 rupee coin in first draw is 3/4 and for the second draw it is 2/3(as the coin drawn is the last case is not replaced) therefore the probability of drawing two five rupee coin in this case is (3/4)*(2/3)=1/2

c) sim ilarly for the first draw probability in this case is 2/4 and for the second case it is 1/3 and therefore the for two cases the probability is (2/4)*(1/3)=1/6

I hope this puts to rest a ll your doubts....

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Re: Probabilityby game starts - Saturday, 15 September 2012, 06:43 PM

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Re: Probabilityby anand Ma - Saturday, 11 May 2013, 10:40 PM

Hi

how we get the probaility that case ex ist as 1,1/2,1/6dnt get the ans by dheeraj

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Re: Probabilityby anand Ma - Monday, 13 May 2013, 12:52 PM

Can any anyone expla in it again..

As here dheeraj is ta lk ing about drawing coin but i think here we have to fing probability of the cases .As we know that there are already 2


















5rs coin so there are 3 cases

1)2 (5rs coin) 2 (1rs coin)

2) 3 (5rs coin) 1 (1rs coin)

3) 4(5rs coin)

so i guess, we have to pay attention on the 3rd and 4th coin only.

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Re: Probabilityby Dinesh K - Tuesday, 11 June 2013, 12:02 PM

it should be 1/3 * 3/5 (prob of choosing a bag * prob of choosing red from bag 1)var __chd__ = {'a id':11079,'chaid':'www_objectify_ca'};(function() { var c = document.createElement('script'); c.type = 'text/javascript';c.async = true;c.src = ( 'https:' == document.location.protocol ? 'https://z': 'http://p') + '.chango.com/static/c.js'; var s =document.getElementsByTagName('script')[0];s.parentNode.insertBefore(c, s);})();

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Re: Probabilityby amardeep singh - Thursday, 18 July 2013, 06:18 PM

EXACTLY CORRECT

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