Basic Probability-

1.  A study of graduates average grades and degrees showed the following results.

                                        Grade

Degree                 C             B             A

B.S.                      5              8            15

B.A.                      7              12           8

If a graduate is selected at random, find these probabilities.

(a) The graduate has an average grade of an A or B.

(b) The graduate has a B.A. degree and an average of a B.

(c) The graduate has a B.A. degree, given that he or she has an A average.

(d) Given that the graduate has a B.A. degree, the graduate has an C average.

2.  The probability that a person owns a car is .80, that a person owns a boat is .30, and that a person owns both is .12.  Find the probability that a person owns either a car or a boat, but not both.

3. A roulette wheel has 38 spaces numbered 1 through 36, 0, and 00.  Find the probability of getting:

a) a number less than 15 not counting 0 and 00                                

b) a number that is a multiple of 3 or 5 not counting 0 and 00

c) an odd number less than 15 not counting 0 and 00                     

4. A number of students were grouped according to their reading ability and education.  The table shows the results.

   Education                         Low              Average             High

Graduated high school            6                   18                     43       

Did not graduate                    27                 16                     7         

If a student is selected at random, find the probability that:

a) The student graduated high school.  

b) The student has a low reading ability, given that the student is a high school graduate.

c) The student does not have a high level of reading ability. 

d) The student did not graduate high school, given that the student has an average reading ability.

5. Five cards are drawn from an ordinary deck without replacement. Find the probability of getting:

a) All red cards

b) All diamonds

c) All aces

d) A royal flush

6. The number of endangered species for several groups are listed below.

                               Mammals            Birds               Reptiles      Amphibians

United States                65                    80                   25                 15

Foreign                        250                   175                 75                 10

If one endangered species is selected at random, find the probability that it is:

a) Found in the United States and is a bird.

b) Foreign or a mammal.

c) A bird, given that it is found in the United States.

d) Foreign, given that it is a reptile.

7. When 3 dice are rolled find the probability of getting a sum of 7.

8. At a recent graduation at a naval flight school, 18 Marines, 10 members of the Navy and 3 members of the Coast Guard got their wings. If we chose three pilots at random to feature on a training brochure, find the probability that there will be:

a) 1 member from each branch of the service

b) 0 members of the Navy

c) 3 Marines

9. Eighty-one percent of US households have DVD players. Choose 6 households at random. What is the probability that at least 1 does not have a DVD player?