Exam I Math 411

Boggess

Spring 1996

Clearly show all work using complete sentences. The clarity of your presentation will be graded along with mathematical correctness. Credit will not be given for unsupported answers. Complicated arithmetic expressions do not need to be simplified. Each question is worth 12 points.

1. How many ways can a professor give two A's, four B's and seven C's to a class of 13 students?
2. Suppose you roll two dice while blindfolded. Your friend tells you that the sum of the two dice is 7. What is the probability that one of the dice shows a 3?
3. Three students are pre-registering for calculus. They have heard there are six good teachers and four bad ones, but they do not know who the good or bad ones are. Each of them registers for a different teacher in the hopes that one of them will get a good one. What is the probability of at least one of the students registering for a good teacher?
4. Suppose you know the following about the three events A, B, and C.

   

   

   1. Are and C pairwise independent?
   2. Are and C independent?

   You must support your answer - a simple yes or no answer will not suffice and you will not receive any credit.

5. What is the probability of obtaining two pairs in a poker hand of 5 cards?
6. Suppose 13 cards are picked at random from a 52 card deck. What is the probability that you will not get a card from every suit? You do not need to simplify your answer.
7. Suppose there are two dice, one of which is fair (6 distinct numbers, 1 thru 6, on its 6 faces) and the other which is a trick die which has two 6's, and one of each of the numbers 1 thru 4. Suppose one of these dice are chosen at random and rolled 10 times. If four sixes appear, what is the probability that the trick die was chosen?
8. Two boys take turns shooting free-throws. John shoots first and makes a basket with probability 1/4. David throws second and makes a basket with probability 1/3. What is the probability John will make a basket before David?

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