Math 431
Exam 1 (with answers)
Spring 2012
1. A fair die is rolled 20 times.
(a) [3 points] What is the probability of 3 sixes in the rst twenty rolls?
Solution: Using the binomial distribution we get
20
3
1
6
3
5
6
17
.
(b) [5 points] What is the probabi
Math 431
Exam 2 (with answers)
Spring 2012
1. John has a 2/3 chance of making a free throw shot on each attempt. His attempts are
independent.
(a) [6 points] What is the probability that it takes him exactly 5 attempts to make 3
free throw shots?
Solution
Math 431
Final Exam (with answers)
Spring 2012
1. [8 points] Two cards are chosen (as usual, without replacement) from a standard deck
of 52 cards. What is the probability that the rst card is a heart given that they are not
both hearts?
Solution: Let A b
Math 431
Final Exam (with answers)
Spring 2012
1. [8 points] Two cards are chosen (as usual, without replacement) from a standard deck
of 52 cards. What is the probability that the rst card is a heart given that they are not
both spades ?
Solution: Let A