1.
It is known that screws produced by a certain company will be defective with probability 0.01 independently of each other. The company sells screws in packages of 10 and offers a money-back guarantee that at most 1 of the 10 screws is defective. If a purchaser finds more than one defective screw in a package, the company will replace the package free of charge. What proportion of packages sold must the company replace?

2.
On average 5.2 hurricanes hit a certain region in a year. What is the probability that there will be 3 or fewer hitting the region this year?

3.
When 3 friends go out for coffee, they decide who will pay the check by each flipping a coin and then letting the â€œodd personâ€ pay. (This is the person whose coin differs from the other two.) If all three flips are the same (so there is no odd person), then they make a second round of flips and continue to do so until there is an odd person. What is the probability that:

A. Exactly three rounds of flips are needed to determine who pays.
B. More than four rounds are needed.

4.
Busses arrive at a specified stop at 15-minute intervals starting at 7 a.m. That is, they arrive at 7, 7:15, 7:30, 7:45, 8, and so on. If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7:30, find the probability that he waits:

A. Less than 5 minutes for a bus.
B. More than 10 minutes for a bus.

5.
A betting game involves the following process: You roll a fair die. If the roll results in a 1, 2, 3, or 4, you draw 4 cards without replacement from a well shuffled standard deck of 52 cards containing 4 aces. If the roll results in a 5 or 6, you draw 6 cards without replacement from a well shuffled standard deck of cards. If the cards you draw contain at least one ace, you win.

A. What is the probability that you win the game?
B. The game costs $5 to play. If you win, you get a total of $10 back (i.e., your original $5 back plus a $5 prize). If you played this game many times, would you expect to make money in the long run? Explain your answer.

6.
Let Y have the density function given by: f(y) = cy2 for 0 â‰¤ y â‰¤ 2
f(y) = 0 elsewhere
A. Find c
B. Find E(Y) and SD(Y)
C. Find F(y) (Reminder: Make sure you define F over the whole real line.)

1. It is known that screws produced by a certain company will be d...