Condo Sales and Interest Rates The probability that condo sales will increase in

Question

Condo Sales and Interest Rates The probability that condo sales will increase in the next 6 months is estimated to be 0.40. The probability that the interest rates on condo loans will go up in the same period is estimated to be 0.65. The probability that condo sales or interest rates will go up during the next 6 months is estimated to be 0.80. a. What is the probability that both condo sales and interest rates will increase during the next six months? b. What is the probability that neither condo sales nor interest rates will increase during the next six months? c. What is the probability that condo sales will increase but interest rates will not during the next six months.

Explanation / Answer

Let A denote probability that condo sales will increase and B denote the probability that condo loans will go up

P(A) = 0.4

P(B) = 0.65

P(A or B) = 0.8

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

a) Probability that both sales and interest rates will increase = P(A and B) = P(A) + P(B) - P(A or B)

= 0.4 + 0.65 - 0.8 = 0.25

(The events are not independent, so you cannot multiply P(A) and P(B) to get P(A and B)

b) P(neither condo sales nor interest rate will increase) = 1 - P(A or B)

= 1 - 0.8

= 0.2

c) P(condo sales will increase but interest rate will not) = P(A) - P(A and B)

= 0.4 - 0.25

= 0.15

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