1. Probability Distributions

2. Problem: Suppose you are taking a true or false test with 6 questions…
Problem: Suppose you are taking a true or false test with 6 questions…. But you didn’t study at all
Take out a coin and a piece of paper – you will flip your coin to answer the following problems.
Heads is true, tails is false.

3. STATISTICS 257 Final Exam – Oh no!
Get out your coin and guess the following: 1. If a gambling game is played with expected value 0.40, then there is a 40% chance of winning.

4. … I lost my notebook…
2. If A and B are independent events and P(A)=0.37, then P(A|B)= 0.37.

5. …the textbook is too heavy
3. If A and B are events then P(A) + P(B) cannot be greater than 1.

6. ... I’m never going to really need this stuff anyway, right?
4. If P(A and B) = 0.60, then P(A) cannot be equal to 0.40.

7. …why are the questions so long?
5. If a business owner, who is only interested in the bottom line, computes the expected value for the profit made in bidding on a project to be -3,000, then this owner should not bid on this project.

8. …. Oops, I left my calculator in my locker
6. Out of a population of 1000 people, 600 are female. Of the 600 females 200 are over 50 years old. If F is the event of being female and A is the event of being over 50 years old, then P(A|F) is the probability that a randomly selected person is a female who is over 50.

9. So how did you do? #1 – False #2 – True #3 – False #4 – True #5 – True
Tally up your responses – Did you pass?

10. The Distribution of scores on the test – why is it more likely to get 3 right than to get 6 right?

11. Try to determine the following probabilities when guessing your answers on a true or false test:
0 right
1right

12. Try to determine the following probabilities when guessing your answers on a true or false test:
0 right
1right
2 right
3 right
4 right
5 right
6 right
x right

13. Probability Distribution for Guessing on 6 True or False Questions

14. The Binomial Probability Distribution
A binomial probability is an experiment where we count the number of successful outcomes over n independent trials
Question: Is guessing the answer on 6 true / false questions a binomial probability?

15. Calculating a Binomial Probability
In general, we can calculate a binomial probability of x successes on n independent trials as:
Eg) What is the probability of guessing 4 out of 6 answers on a true or false quiz?

16. Try the following:
You are shooting 8 free throws and you have a 75% of scoring on each. What is the probability that you will:
Score on 0 shots?
Score on 1 shot?

17. Try the following:
You are shooting 8 free throws and you have a 75% of scoring on each. What is the probability that you will:
Score on 0 shots?
Score on 1 shot?
Score on 2 shots?
Score on at least 2 shots?

18. You are shooting 8 free throws and you have a 75% of scoring on each
You are shooting 8 free throws and you have a 75% of scoring on each. What is the probability that you will:
5. Score at least 7 shots? 6. Score 6 or 7 shots? 7. Score all of your shots except the last one?

19. You are shooting 8 free throws and you have a 75% chance of scoring on each.
How many shots do you expect to score?

20. The Expected Value of a Binomial
In general, the expected value of a binomial probability is given as:
Try: What is the expected value of
Guessing on 100 True / false questions?
Rolling a dice 600 times and counting 6s?
Shooting 200 baskets with a 75% chance of making each one

21. Try the following:
Suppose that 2% of all calculators bought from Dollarama are defective.
You randomly collect 20 of them.
What is the probability that:
None of them are defective?
2 or more are defective?
In a batch of 1500, how many do you expect to be defective?

22. Summary: What is a probability distribution?
How do you calculate a binomial probability?
What are two conditions that you need in order to use a binomial probability calculation?
Why do you multiply a binomial probability by nCx?
p. 385 #1, 2, 3, 5, 6bc, 7ab, 8ab, 15, 17 Challenge: 10, 11