MATH 230

TEST II

Fall 1999

Bellamy & Williford

Problems 1-4 are worth 25 points each.

1. A club has 14 members, six men and eight women. A planning committee of three chosen randomly from the membership.
   1. Describe explicitly a suitable equiprobable sample space for this experiment.
   2. Find the probability that the planning committee is all male.
   3. Find the probability that the planning committee members are all the same sex.
   4. Find the conditional probability that the planning committee members are all male given that they are all the same sex.
   5. Find the conditional probability that the committee has at least two men on it, given that the members are not all the same sex.

2. Consider two events, A and B, in a sample space S. Assume Find under each of the following additional assumptions:
   1. A and B are disjoint.
   2. A and B are independent.
   3. 
   4. 
   5. 
      
      (Note: At least one of the above is impossible. Be sure to clearly identify it as such.)

3. Three fair dice are rolled, one red, one blue, and one yellow. Find:
   1. The probability that all three numbers are different.
   2. The probability that all three numbers are the same.
   3. The conditional probability that all three numbers are different given that they are not all the same.

4. Let E and F be independent events in a sample space S. If find:
   1. 
   2. 
   3. 
   4. 

5. Bonus: 15 quiz points

   Ten people, including Sally and Bill, are seated in a random order on a long bench. Find the probability that Sally and Bill are side by side.