What are Your Chances?What are Your Chances?

By AlexanderBy Alexander

3/14/20063/14/2006

Homework MadnessHomework Madness

In this part of the unit we pulled out cubes In this part of the unit we pulled out cubes from two bags and recorded our results on from two bags and recorded our results on a calendar thingingy. The bags were a calendar thingingy. The bags were labeled “H” and “T”. labeled “H” and “T”.

This was our probability for the first part; This was our probability for the first part; P(Homework)=12/20 and P(No P(Homework)=12/20 and P(No Homework)= 8/20.Homework)= 8/20.

The second part of Homework Madness’ The second part of Homework Madness’ probability was; P(NH)=15/20 and probability was; P(NH)=15/20 and P(H)=5/20.P(H)=5/20.

Place Your ChipsPlace Your Chips

In this unit we used small game In this unit we used small game boards, which we placed little chips boards, which we placed little chips on and rolled a number cube 36 on and rolled a number cube 36 times.times.

We removed a chip on each row We removed a chip on each row when we rolled that number.When when we rolled that number.When there were no more chips in the there were no more chips in the column, we couldn’t remove any column, we couldn’t remove any chips from that column.chips from that column.

Sums and ProductsSums and Products We didn’t do very We didn’t do very

much in this unit, but much in this unit, but we did learn why 7 is we did learn why 7 is most peoples lucky most peoples lucky number.number.

7 is most peoples 7 is most peoples lucky number because lucky number because it has the most it has the most possible outcomes on possible outcomes on two number cubes: 1 two number cubes: 1 and 6, 2 and 5, 3 and and 6, 2 and 5, 3 and 4, 3 and 4, 5 and 2, 4, 3 and 4, 5 and 2, and 1 and 6.and 1 and 6.

Odd or EvenOdd or Even

In this unit we spun two spinners, Spinner In this unit we spun two spinners, Spinner A and Spinner B, 16 times and we A and Spinner B, 16 times and we recorded our results.recorded our results.

I was paired with Stephanie, and we I was paired with Stephanie, and we accidentally did this too many times.accidentally did this too many times.

We found out that even though it seemed We found out that even though it seemed the even numbers had a larger chance the even numbers had a larger chance than odd numbers, they both had the than odd numbers, they both had the same probability of happening.same probability of happening.

The Carnival of ChanceThe Carnival of Chance

In this unit we got to create a In this unit we got to create a slightly unfair carnival game.slightly unfair carnival game.

I was paired with Saman, and we I was paired with Saman, and we chose a bag with dice, so we had to chose a bag with dice, so we had to make a dice rolling game.make a dice rolling game.

The slightly unfair game turned out The slightly unfair game turned out to be really unfair, one-hundred to be really unfair, one-hundred something to thirty or forty something to thirty or forty something.something.

2 in 282 in 28 The game Saman and I created was 2 in 28. In The game Saman and I created was 2 in 28. In

this game you roll 27 number cubes and you have this game you roll 27 number cubes and you have 28 chips. All the chips must be on a game board 28 chips. All the chips must be on a game board that has the numbers 1-6. Once all the chips are that has the numbers 1-6. Once all the chips are down, you roll all 27 number cubes at the same down, you roll all 27 number cubes at the same time (we had a cup). What ever the amount of time (we had a cup). What ever the amount of number cubes that were on a certain number, number cubes that were on a certain number, that is how many chips you remove from a that is how many chips you remove from a column. If there are more cubes than chips, you column. If there are more cubes than chips, you can only take off all the chips in that column. If can only take off all the chips in that column. If you are left with 0,1,or2 chips, you win. If there you are left with 0,1,or2 chips, you win. If there are more, better luck next time.are more, better luck next time.

What I LearnedWhat I Learned

I learned that probability is the I learned that probability is the chance of something happening, like chance of something happening, like a coin landing on heads (50%). These a coin landing on heads (50%). These units really helped me learn units really helped me learn probability. I think this unit was my probability. I think this unit was my favorite all year.favorite all year.

GlossaryGlossary

Certain Event-an event that will definitely happenCertain Event-an event that will definitely happenComposite Number-a number that has more than Composite Number-a number that has more than

two unique factorstwo unique factorsCompound Number-combination of two or more Compound Number-combination of two or more

simple independent events such as rolling two simple independent events such as rolling two number cubes or tossing a coin and spinning a number cubes or tossing a coin and spinning a spinnerspinner

Equally Likely-two or more possible outcomes of a Equally Likely-two or more possible outcomes of a given situation that have the same chance of given situation that have the same chance of occurring or the same probability. An equally occurring or the same probability. An equally likely event, such as tossing a heads using a fair likely event, such as tossing a heads using a fair coin, has a probability of ½.coin, has a probability of ½.

More GlossaryMore Glossary

Even Number-a multiple of 2, i.e. 0, 2, 4, …Even Number-a multiple of 2, i.e. 0, 2, 4, …Experimental Probability-a statement of probability Experimental Probability-a statement of probability

based on the results of a series of trialsbased on the results of a series of trialsFair Game-a game in which the theoretical Fair Game-a game in which the theoretical

probability of each player winning is equally likelyprobability of each player winning is equally likelyFavorable Outcome-outcome of interest in a Favorable Outcome-outcome of interest in a

probabilistic situationprobabilistic situationLaw of Large Numbers-states that experimental Law of Large Numbers-states that experimental

probabilities collected over many trials will probabilities collected over many trials will predict the theoretical probabilities only when a predict the theoretical probabilities only when a very large number of trials are conductedvery large number of trials are conducted

Odd Number-a number that has a remainder of 1 Odd Number-a number that has a remainder of 1 when dividing by 2when dividing by 2

Even More GlossaryEven More Glossary

Possible Outcomes-all of the possible numbers or results of an Possible Outcomes-all of the possible numbers or results of an action. For instance, the possible outcomes from rolling a action. For instance, the possible outcomes from rolling a number cube are 1, 2, 3, 4, 5, and 6.number cube are 1, 2, 3, 4, 5, and 6.

Probability-the chances of an event happening. Probability is Probability-the chances of an event happening. Probability is often represented as a number. This can be expressed as often represented as a number. This can be expressed as 0(impossible), 1(certain), or a fraction in between 0 and1.0(impossible), 1(certain), or a fraction in between 0 and1.

Product-the answer to a multiplication problemProduct-the answer to a multiplication problemSystematic (Organized) List-a list of data of any sort that is Systematic (Organized) List-a list of data of any sort that is

arranged in such way as to minimize omitting any member arranged in such way as to minimize omitting any member of the listof the list

Theoretical Probability-a statement of probability based on Theoretical Probability-a statement of probability based on analysis of a situationanalysis of a situation

P(event)=P(event)=number of favorable outcomesnumber of favorable outcomes number of possible outcomesnumber of possible outcomes

Tree Diagram (counting tree)-visual method of listing Tree Diagram (counting tree)-visual method of listing combinations or outcomescombinations or outcomes

Extra GlossaryExtra Glossary

Trial-one round of an experimentTrial-one round of an experiment

Unequally Likely-two or more outcomes that Unequally Likely-two or more outcomes that do not have the same chance of occurring do not have the same chance of occurring or that do not have the same probability. or that do not have the same probability. For example, in a bag that holds three For example, in a bag that holds three cubes, two that are green and one that is cubes, two that are green and one that is yellow, the probability of randomly select yellow, the probability of randomly select a green cube is 2/3 and a yellow cube is a green cube is 2/3 and a yellow cube is 1/3.1/3.

M3-Good Points, Bad PointsM3-Good Points, Bad Points

I really liked the probability unit the best yet, I really liked the probability unit the best yet, especially since we got to create a slightly especially since we got to create a slightly unfair carnival game. What is really good unfair carnival game. What is really good about M3 is it challenges people who are about M3 is it challenges people who are really good at math. I really think it should really good at math. I really think it should keep going. The only thing I would suggest keep going. The only thing I would suggest is a smaller amount of Think Deeplys. They is a smaller amount of Think Deeplys. They are good, but I think there should be a are good, but I think there should be a slightly smaller amount, like no beginning slightly smaller amount, like no beginning activity not in the book and having Think activity not in the book and having Think Deeplys as the first few pages.Deeplys as the first few pages.

THE ENDTHE END