Question

An investor purchased 100 shares of Fifth Third Bank stock and 100 shares of Santee Electric Cooperative stock. The probability the bank stock will appreciate over a year is 0.70. The probability the electric utility will increase over the same period is 0.60. Assume the two events are independent.a. What is the probability both stocks appreciate during the period?
b. What is the probability the bank stock appreciates but the utility does not?
c. What is the probability at least one of the stocks appreciates?

Answer 1

Answer:

(a) 0.42

(b) 0.28

(c) 0.88

Step-by-step explanation:

Let probability that the bank stock will appreciate over a year, P(A) = 0.70

Probability that the electric utility will increase over the same period, P(B) = 0.60

Also, it is given that the two events are independent.

(a) Probability that both stocks appreciate during the period = Bank stock will appreciate * Electric utility will appreciate = P(A) * P(B)

     = 0.70 * 0.60 = 0.42 .

(b) Probability that the bank stock appreciates but the utility does not is given by;

     P(A) * (1 - P(B)) = 0.70 * (1 - 0.60) = 0.70 * 0.40 = 0.28 .

(c) Probability that at least one of the stocks appreciates = P(A $\bigcup$ B)

    P(A $\bigcup$ B) = P(A) + P(B) - P(A $\bigcap$ B)

                   = 0.70 + 0.60 - (0.70 * 0.60)   { because both events are

                                                                           independent }

                   = 1.3 - 0.42 = 0.88 .