Math 230

Test I

Bellamy & Sullivan

Fall 1998

Show all work! Point values are as indicated. Only problems 4 and 6 require arithmetic; in problem 6, give your answers as fractions in lowest terms.

1. Let Let . (Note that are ordered pairs; thus n(A)=n(B)=3).

   List all the elements in:

   
   
   

2. Four Microsoft customers are chosen randomly from a set of 100 customers previously surveyed. If 12 of the 100 were dissatisfied with a certain application program, what is the probability that all four of those chosen now were satisfied in the initial survey? (No arithmetic needed!)

3. Two fair dice, one red and one green, are rolled.
   1. Describe the standard 36-element sample space S.
   2. Find the conditional probability doubles are rolled given that the sum obtained is even.
   3. Find the conditional probability the sum is even given that doubles are rolled.

4. Compute exactly: you must show (indicate) what arithmetic you are doing, but you may use a calculator to do it.

   
   
   

5. A club has 17 members, of whom 3 are licensed pilots and four are medical doctors. One is both a pilot and an M.D. A committee of 4 is to be chosen from this club.
   1. How many different committees are possible?
   2. How many different committees are possible which include at least one M.D.?
   3. How many different committees are possible which include at least one pilot?
   4. How many different committees are possible which include neither pilots nor M.D.'s?

6. In a sample space are independent events, and .

   Find .