Exercises. b) Are the events A and B independent?

1. Suppose that , , and

a) Find .

b) Are the events A and B independent? Why or why not?

2. Suppose that , , and . Find

a) The conditional probability that B occurs, given that A occurs.

b) The conditional probability that B does not occur given that A occurs.

c) The conditional probability that B occurs given that A does not occur.

3. Concerning the events A and B, the following probabilities are given

; ; .

Determine

a) ; b) ; c)

4. In a study of television viewing habits among married couples, a researcher found that for a popular Saturday night program 25% of the husbands viewed the program regularly and 30% of the wives viewed the program regularly. The study found that for couples where the husband watches the program regularly 80% of the wives also watch regularly.

a) What is the probability that both husband and wife watch the program regularly?

b) What is the probability that at least one-husband or wife-watches the program regularly?

c) What percentage of married couples do not have at least one regular viewer of the program?

5. Of 20 rats in a laboratory, 12 are males and 9 are infected with a virus. Of the 12 male rats, 7 infected with the virus. One rat is randomly selected from the laboratory.

a) If the selected rat is found to be infected, what is the probability that it is a female?

b) If the selected rat is found to be a male, what is the probability that it is infected?

c) Are the events “the selected rat is infected” and “the selected rat is male” independent? Why or why not?

6. Suppose , .

a) Determine if A and B are independent.

b) Determine if A and B are mutually exclusive.

c) Find if A and B are mutually exclusive.

7. An urn has three red and five blue balls. Suppose that 8 balls are selected at random and with replacement. What is the probability that the first three are red and the rest are blue balls?

Answer

1. a) ; ; =0.67; b) No;

2. a) 0.471; b) 0.529; c) 0.719; 3. a) 2/7; b) 32/63; c) 9/16; 4. a) 0.2;

b) 0.35; c) 65%; 5. a) 2/9; b) 7/12; c) No; 6. a) 0.61; b) 0.72; c) 0.641;

7. 0.00503;

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