Math 251, Spring 2002, Exam II
1. A local pizza place offers ÒnoonerÓ pizzas where patrons must choose one of three cheeses, one of three meats and one of eight vegetable toppings. No substitutions are allowed!
(a) (3 pts) How many different ways can one make a pizza? Explain your answer.
(b) (2 pts) How many different ways can one make a ÒnoonerÓ pizza where cheddar is chosen as the cheese, and ham is chosen as the meat?
2.(6 pts) The ÒMinibucksÓ lottery is one where the ticket purchaser must choose 5 numbers out of 21 where the order doesnÕt matter.
(a) Find the total number of ticket combinations possible.
(b) Find the number of ways that a ticket can match 3 of the 5 winning numbers.
(c) What is the probability that a randomly selected ticket will match 3 of the 5 winning numbers.
3. The following characteristics of a purse snatching couple (events) were described by a
prosecutor in court (1964 in Los Angeles) as having the following probabilities.
Event Probability
E1=drives a yellow car 1/10
E2=man has a mustache 1/4
E3=woman has a ponytail 1/10
(a) (2 pts) Assuming the above events are independent, find the probability that a randomly selected couple is a man with a mustache and a woman with a ponytail driving in a yellow car.
(b) (3 pts) Assuming the above events are independent, find the probability that given a randomly selected couple, the woman has a ponytail or the man has a mustache.
(c) (2 pts) If the events E1 and E2 above are independent, must they be mutually exclusive?
4.Suppose a certain type of laser eye surgery has a 96% success rate. Suppose that this surgery is performed on 17 patients and the results are independent of one another.
(a) (2 pts) What is the probability that all 17 of the surgeries will be successful?
(b) (2 pts) What is the probability that exactly 16 of the surgeries will be successful?
(c) (2 pts) What is the probability that 15 or fewer of the surgeries will be successful?
(d) (2 pts) Find the mean and standard deviation for the expected number of successes if the surgery is performed 50 times?
5. (4 pts) A 5th grade class holds a raffle in which it sells 5000 tickets at $10 a piece. They will give 1 prize of $1000, 2 prizes of $500, and 7 prizes of $100, and 10 prizes of $50. Complete the following table for the probability distribution for the net expected winnings x given that 1 ticket is purchased; note the net winnings for the prize of $1000 is $990 because the ticket price is subtracted, and so on.
x 9904909040-10
P(x).0002
What are the expected net earnings of one ticket?
6.Consider the random variable x with the following probability distribution.
x 5 7 9 10
p(x).2 .25 .15 .4
(a) (4 pts) Find the mean and standard deviation of x.
(b) (2 pts) Sketch a probability histogram for x.