Copyright©Ed2NetLearning.Inc 1 Theoretical Probability.

Copyright©Ed2NetLearning.Inc 1

Theoretical Probability

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Previous Knowledge

Write each fractions to their lowest terms:

1. 14/21 = 2/3

2. 9/12 = ¾

3. 10/15 = 2/3

4. 12/16 = ¾

5. 7/35 = 1/5

6. 4/6 = 2/3


Previous Knowledge

Write in simplest forms:

1. 5/6 x 3/10 = ¼

2. 3/6 x 4/12 = 1/6

3. 2/11 x 5/6 = 5/33

4. 7/3 x 4/11 = 28/33


Objective

To find the possibility of happening of a particular result of an incident.


Some Definitions Before we study probability we must be familiar

with some terms. When we are tossing a coin, we will get either

HEAD or TAIL. Getting HEAD or TAIL is called OUTCOMES

Experiment : An activity which gives some well-defined outcomes.

Random Experiment: An experiment whose outcome cannot be predicted in advance.

When we toss a coin, we cannot predict that we shall get head or tail.

Events: The possible outcomes of a trial are called events. The out come HEAD or TAIL is an event or favorable outcome.


Theoretical Probability

It is the chance that some event will occur.

OR

Probability is the measure of the chance of an event happening.


Definition of Theoretical Probability

Theoretical Probability of an event is a ratio that compares the number of favorable outcomes to the number of possible outcomes.

Symbol used for probability is

P(event) = number of favorable outcomes

number of possible outcomes.


Properties of Probability The probability that an event will occur is a number

from 0 to 1, including 0 and 1.

0 ¼ ½ ¾ 1

Impossible to occur Equally likely to occur Certain to occur


Find Probability Find the probability of drawing 3 from a

collection of 5 flash cards

Probability of drawing 3 is P(3) = number of favorable outcomes

number of possible outcomes

= 1/5

1 2 3 4 5


Example – 2

A coin is tossed. What is the probability of getting a head?

P(head) = number of favorable outcomes


Here, the favorable out come is getting head, therefore number of favorable outcome is 1. The number of possible outcomes are head and tail. That is equal to 2.

P(head) = ½


Now your turn

A die is thrown. What is the probability that

1. Face 5 appears

P(5) = 1/6

2. Face 7 appears

P(7) = 0


Representing probability in a line

Represent the probability of a cat giving birth to a dog. P(C)

0 ¼ ½ ¾ 1

P(C)


Let’s try to represent in a line

The chance that a girl is chosen from a group of 2 girls and 6 boys. P (G)

P(2 girls) =2/8 = ¼

0 ¼ ½ ¾ 1

P(G)


Complementary Events

Complementary Events are two events in which either one or the other must happen at the same time.

For example, a coin landing on heads or not landing on heads. The sum of the probabilities of complementary events is 1.


Use of Probability In today’s weather news, it is reported that

there will be a chance of 30% rain. What is the probability that it will not rain?

Two events are complementary. So, the sum of the probabilities is 1.

P(rain) + P(not raining) = 1 30/100 + P(not raining) = 1

P(not raining) = 1 – 30/100 = 70/100 = 7/10


Now solve this

In a motor race competition the Lions predicted that there is a ¾ chance of winning the race. What is the probability of losing the race?

P(wins) + P(fails) = 1 P(fails) = (1 – ¾ )

= ¼


Practice and Applications

i) In a spinner of 5 colors, what is the probability that the arrow lands on red?

P (red) = 1/5.

Violet RedBlackYellowGreen


Practice and Applications

Mark the probability in a line:

ii) If a spinner with 4 colors ( red,blue, yellow, green) is rotated, the chance that green will show up [P(G)]

P( green ) = ¼

0 ¼ ½ ¾ 1

P(G)


REVIEW Probability is the measure of the chance of an event happening.

Theoretical Probability of an event is a ratio that compares the number of favorable outcomes to the number of possible outcomes.

Symbol used for probability is

P (event) = number of favorable outcomes



ASSESSMENT1. Six candidates appear for an interview, only one

candidate is to be selected. What is the probability of A being selected when A is one of the 6 candidates?P(A) = 1/6

2. In a bag, there are 7 cards bearing numbers 1 to 7. A card is picked up at random. What is the probability of picking i) 3 ii) odd number iii) even number iv) prime number.i) P(3) = 1/7ii) odd numbers are 1,3,5,7; P(Odd) = 4/7iii) even numbers are 2, 4, 6; P(even) = 3/7iv) Prime numbers are 2, 3, 5, 7

P (prime number) = 4/7


Assessment3) A die is thrown. What is the probability of getting a number less than 7?

less than 7 means 1,2,3,4,5 and 6. Probability of getting either 1,2,3,4,5 or 6 = 6/6 = 1

4) A coin is tossed once. What is the probability of getting i) a tail?P (Tail) = ½

5) A bag contains 2 red, 3 blue and 5 black balls. A ball is drawn at random. What is the probability of drawing (i) a red ball (ii) a blue ball and a (iii) white ball?Total number of balls = 2 + 3 + 5 = 10(i) Favorable outcomes = 2 red balls

P( a red ball) = 2/10 = 1/5(ii) Favorable Outcomes = 3

P( a blue ball) = 3/10(iii) Favorable outcomes = 5

P( a white ball) = 5/10 = ½


Assessment6) The letters of the word “PROBABILITY” are placed in a bag. One

letter is taken out at random. What is the probability that letter picked up is

(i) A (ii) B (iii) I (iv) P (v) C (vi) ANY?

P(A) = 1/11

P(B) = 2/11

P(I) = 2/11

P(P) = 1/11

P(C) = 0

P(ANY) = 1

7) A die is thrown. What is the probability of rolling ‘two, three, five or six’ ?

P(2 , 3, 5 or 6) = 4/6 = 2/3


Assessment8. Write the probability for the following statements.

i. There are 10 beads in a bag. One bead is black and the rest are white. A bead is picked up. What is the probability of picking a black bead?

P (black bead) = 1/10

ii. The sun will rise from north today.

P ( sun will rise from north today) = 0

9. From a pack of playing cards, a card is drawn. Find the probability of getting a red card ?

P ( red card) = ½

10. In an octagonal spinner, 1, 2, 3, 4, 5, 6, 7 and 8 arre marked on it. Write the probability hen the spinner lands on any number less than 9.

P( spinner lands on any number less than 9) = 8/8 = 1


Great Job!

Copyright©Ed2NetLearning.Inc 1 Theoretical Probability.

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