9.79. Suppose we keep drawing cards from a deck of 52 cards with replacement until we see two face cards (Jack, Queen, or King) or two number cards (ranks one through ten).

1. What is the sample space of this experiment?

2. What is the probability function?

3. What is the probability that the experiment ends with two face cards?

9.79. Suppose we keep drawing cards from a deck of 52 cards with replacement until we see two face cards (Jack, Queen, or King) or two number cards (ranks one through ten).

1. What is the sample space of this experiment?

2. What is the probability function?

3. What is the probability that the experiment ends with two face cards?

1. Inmates According to Harper’s Index, 53% of all federal inmates are serving time for drug dealing. A random sample of 6 federal
inmates is selected.
(a) What is the probability that 4 or more are serving time for drug dealing?

(b) What is the probability that 5 or fewer are serving time for drug dealing?

(c) What is the expected number of inmates serving time for drug dealing?

13. According to Harper’s Index, 50% of all federal inmates are serving time for drug dealing. A random sample of 16 federal inmates is selected. (a) What is the probability that 12 or more are serving time for drug dealing? (b) What is the probability that 7 or fewer are serving time for drug dealing? (c) What is the expected number of inmates serving time for drug dealing?

(22 pts) Find the experimental probability of rolling each sum. Fill out the following table:

Suppose the number of customers arriving in a bookstore is Poisson distributed with a mean of 2.3 per 12 minutes. The manager uses a robot to observe the customers coming to the bookstore. a)What is the mean and variance of the number of customers coming into the bookstore in 12 minutes? b)What is the probability that the robot observes 10 customers come into the bookstore in one hour? c)What is the probability that the robot observes at least one customer come into the bookstore within half an hour?

Suppose the time a customer spends in the bookstore is exponentially distributed with a mean of 8 minutes. d) Lisa arrives in the bookstore at 8:00 am, what is the probability that Lisa leaves between 8:04 and 8:05 am? e) Suppose the robot finds Lisa has been in the bookstore for 5 minutes and Jimmy has been in the bookstore for 6 minutes. Conditioned on that, what is the probability that Jimmy leaves the bookstore before Lisa? f) Suppose the robot has been observing the customers in the bookstore for one year, and finds that 50% of the customers will stay in the bookstore for k minutes. What is the value of k?

On Monday mornings, a CIBC branch has only one teller window open for deposits and withdrawals. Experience has shown that the average number of arriving customers in a four-minute interval on Monday mornings is 2.6, and each teller can serve more than that number efficiently. The random arrivals at this bank on Monday mornings are Poisson distributed.

(a) Suppose the teller can serve no more than four customers in any 4-minute interval at this window on a Monday morning. What is the probability that, during any given four-minute interval, the teller will be unable to meet the demand? What is the probability that the teller will be able to meet the demand?

(b) When demand cannot be met during any given interval, a second window is opened. What percentage of the time will a second window have to be opened?

(c) What is the probability that exactly three people will arrive at the bank during a two-minute period on Monday mornings to make a deposit or a withdrawal?

(g) What is the probability that five or more customers will arrive during an eight-minute period?

1. Imagine that you were to shoot a basketball 10 times and you wanted to record the number of shots made.

A.) List an example of an event. (An event is any collection of results/outcomes of a procedure)

B.) List an example of a sample space. (A sample space is a procedure consisting of all simple events)

**I tried this one on my own already but I wanted additional help to see if I was doing this correctly and had the right answer.

5. If I rolled a 4 sided die followed by flipping a coin, what is the probability that I roll an even number followed by getting heads?

6. If the probability of Mr. Hansen makes a three point shot is 10%, what is the probability that Mr. Hansen misses two three point shots in a row?

**Both 5 and 6 events are independent

7. If an event A is making at least one basketball shot, what is the A^c?(A compliment)

**I have the hardest time on probability problems similar to 5 and 6, so please explain along with the answer. Thank you in advance!

Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 55% of all people who take the state bar exam pass. Let n = 1, 2, 3, ... represent the number of times a person takes the bar exam until the first pass.

(a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.)
P(n) =

(b) What is the probability that Bob first passes the bar exam on the second try (n = 2)? (Use 3 decimal places.)


(c) What is the probability that Bob needs three attempts to pass the bar exam? (Use 3 decimal places.)


(d) What is the probability that Bob needs more than three attempts to pass the bar exam? (Use 3 decimal places.)


(e) What is the expected number of attempts at the state bar exam Bob must make for his (first) pass? Hint: Use μ for the geometric distribution and round.