Question

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events increase in house sales and increase in interest rates in the next 6 months are

A. None of the above. B. collectively exhaustive. C. independent. D. mutually exclusive.

Answer 1

Lets say, P(A) = P(House sales will increase in the next 6 months) = 0.25

P(B) = P(Interest rates on housing loans will go up in the next 6 months) = 0.74

Thus, P(A or B) = P(House sales will increase in the next 6 months OR Interest rates on housing loans will go up in the next 6 months) = 0.89

Now , we have

P(A or B) = P(A) + P(B) - P(A and B)

Thus, 0.89 = 0.25 + 0.74 - P(A and B)

Thus, P(A and B) = 0.10

Thus, A and B are not independent and they are not mutually exclusive

Also 1 - P(A or B) = 1 - 0.89 = 0.11 which is not 0

Thus, they are not collectively exhaustive

Thus, correct answer is

A. None of the above