1. JV Stats #6
Simulation, Conditional Probability, Independent Events, Mutually Exclusive Events

2. Simulation
In a high school basketball game, the teams star player misses 2 free throws in a row toward the end of the game and they lose to their rival.
The star player was an 80% free throw shooter. This means that 80% of the time she will make a free throw.
The next few days at school some of her classmates and friends said that she “choked” and missed the free throws because she couldn’t handle the pressure……Is this a fair assumption that she was nervous?
Simulate the chance of her missing 2 shots using probability.

3. Choose one of these methods to perform 10 more repetitons
We need to simulate this player shooting 2 shots.
How can this be done with a random digit table?
Perform 10 repetitions of 2 shots.
Explain how to simulate this with the following:
Calculator
6-sided die
12-sided die
20-sided die
Deck of Cards
An App?
Choose one of these methods to perform 10 more repetitons

5. Simulation
In a high school basketball game, the teams star player misses 2 free throws in a row toward the end of the game and they lose to their rival.
The star player was an 75% free throw shooter. This means that 75% of the time she will make a free throw.
The next few days at school some of her classmates and friends said that she “choked” and missed the free throws because she couldn’t handle the pressure……Is this a fair assumption that she was nervous?
Simulate the chance of her missing 2 shots using probability.

6. Choose one of these methods to perform 10 more repetitons
We need to simulate this player shooting 2 shots.
How can this be done with a random digit table?
Perform 10 repetitions of 2 shots.
Explain how to simulate this with the following:
Calculator
6-sided die
12-sided die
20-sided die
Deck of Cards
An App?
Choose one of these methods to perform 10 more repetitons

8. Here is the situation: Disney is teaming up with McDonalds on a new promotion. In every “happy meal” purchased you will also receive one of 5 Disney character toys(Mickey, Donald, Goofy, Pluto, and Daisy)
The claim from both McDonalds and Disney is that you have an equally likely chance of getting any of these toys in a “happy meal”.
Mr. Pines is irritated after it takes him 19 “happy meals” until his daughter had the entire set. Does he have reason to be irritated? Answer this question using simulation.
Run the simulation 10 times with your group using one of the following techniques:
Calculator, 6-sided die, 12-sided die, 20-sided die, Deck of Cards, Names in a hat, an App.

9. Results from many repetitions of this situation.

10. Expected Value is what you expect to get in the long run.

11. Rolling 2 Dice
How many different outcomes are there for rolling two dice?
List them.

12. Sum 2 3 4 5 6 7 8 9 10 11 12
Sum 2 3 4 5 6 7 8 9 10 11 12
Prob
1/36
1/18
1/12
1/9
5/36
1/6
What is the probability of rolling each sum?
Rolling 2 Dice

13. Sum 2 3 4 5 6 7 8 9 10 11 12
Prob
1/36
1/18
1/12
1/9
5/36
1/6
What is the expected value? In other words, what would you expect to average if you rolled the dice many times?
Rolling 2 Dice

14. It should not be surprising that 7 has the highest probability of occuring. Many games that involve 2 dice are based around getting a sum of 7.
Dice
Craps
Monopoly
SEVEN

16. Rolling 2 Dice What is the probability of rolling doubles?
What is the probability of rolling a sum of 3 or a sum of 9?
What is the probability of rolling a sum less than 9 or doubles?

17. The “OR” Formula
both OR

18. Rolling 2 Dice What is the probability of rolling a sum less than 13?
What is the probability of rolling a doubles or a sum more than 5?
What is the probability of rolling an even sum?

19. Rolling 2 Dice What is the probability of rolling a sum more than 3?
What is the probability of rolling a sum 3 or less?
What is the probability of rolling a sum that is prime?
What is the probability of rolling a sum that is divisible by 3?

20. How much do you expect to win……or lose in the long run.
PAYOUT

21. Create a probability distribution table for this game. ¼
A certain casino game involves drawing different color balls out of a bag. There are 8 balls in a bag: 5 red, 2 blue, and 1 green. If a player draws out a blue ball they win $3 and $20 if they pull out the green ball. If they draw out a red ball they win nothing.
Create a probability distribution table for this game.
Ball
Red
Blue
Green
Probability
5/8
1/8
$Payout $0 $3
$20

22. What is your expected payout for this game?
Ball
Red
Blue
Green
Probability
5/8
1/8
$Payout $0 $3
$20
What is your expected payout for this game?
What would be your expected profit if you had to pay $2 to play?
If you are the casino manager, how much should you charge to play this game in order to maintain a profit in the long run?

23. As a group, create a casino or carnival type game that is new(not a current game)
Be creative, silly, anything.
There must be a cost to play, a realistic price.
Create a probability distribution table for this game.
Best game earns cards.

24. Mutually Exclusive Events
Independent Events
* Events are independent if one event has nothing to do with another event
Flipping coins are independent events, the next flip has nothing to do with the previous flip…..coins have no memory!
Mutually Exclusive Events
* Two events cannot both happen at the same time
The event of rolling a 3 and the event of rolling doubles are mutually exclusive, they cannot both happen at the same time.

25. Mutually Exclusive Events
Independent Events
* Events are independent if one event has nothing to do with another event
P(A and B) = P(A)P(B)……multiply them
Mutually Exclusive Events
* Two events cannot both happen at the same time
P(A and B) = 0…….cannot both happen

26. Rolling 2 Dice
What is the probability of rolling a 2 on your first roll and then a 7 on your second roll?
P(rolling a 2) = 1/36
P(rolling a 7) = 1/6
These events are independent
Multiply them (1/36)(1/6) = 1/216
What does 1/216 mean in this situation?
It means that this would happen about once in 216 tries at rolling 2 dice two turns in a row.

27. A car dealership services the cars it sells
A car dealership services the cars it sells. The mechanics use a two step procedure to locate the problem immediately when the car is brought in. Step I locates the problem with a probability of 0.8. Step II is employed if Step I fails; it locates the problem with a probability of 0.6. What is the probability that when a car is brought in, the problem will not be located?
Use a Tree Diagram

28. A car dealership services the cars it sells
A car dealership services the cars it sells. The mechanics use a two step procedure to locate the problem immediately when the car is brought in. Step I locates the problem with a probability of 0.8. Step II is employed if Step I fails; it locates the problem with a probability of 0.6. What is the probability that when a car is brought in, the problem will be located?
Use a Tree Diagram

29. Solution

30. Solution

31. A golfer has a 0.9 probability of choosing the correct club; if so he has a 0.5 probability of making a good shot. If he chooses the wrong club, he has a 0.1 probability of making a good shot. What is the probability he’ll make a good shot?
Use a Tree Diagram

32. solution

33. A golfer has a 0.9 probability of choosing the correct club; if so he has a 0.5 probability of making a good shot. If he chooses the wrong club, he has a 0.1 probability of making a good shot. What is the probability he chose the correct club given he made a good shot?
Diferent question here, the word GIVEN implies the use of a conditional probability formula

34. solution

35. As a group, create a similar “tree type” probability problem.
Be creative, silly, anything.
Check with me on your math, I will tell you if it is a valid problem.
Best problem earns cards.

36. A check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had TV’s, and 21% had both a TV and a refrigerator, What’s the probability that a randomly selected dorm room has…..
We need to draw out this situation
A TV but no refrigerator
A TV or a refrigerator
A TV or a refrigerator, but not both
Neither a TV nor a refrigerator

37. The “Or” Formula
both OR
The “Given” Formula

38. Mutually Exclusive Events
Independent Events
* Events are independent if one event has nothing to do with another event
P(A and B) = P(A)P(B)……multiply them
Mutually Exclusive Events
* Two events cannot both happen at the same time
P(A and B) = 0…….cannot both happen

39. A check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had TV’s, and 21% had both a TV and a refrigerator, What’s the probability that a randomly selected dorm room has…..
A TV but no refrigerator
A TV or a refrigerator
A TV or a refrigerator, but not both
Neither a TV nor a refrigerator
A TV given they have a refrigerator
A refrigerator given they have a TV

43. The Rancho Alamitos Baseball team plays about 52% of their games at “home”. When they are playing at “home” they win about 78% of the time. When they are playing “away” they lose about 32% of the time.
a) Complete the tree diagram to represent this situation.
b) What is the probability that the team wins a randomly selected game?
c) What is the probability that they were playing at home given they lost a game?