Answer to Question #165986 in Statistics and Probability for Mehrdad Safizadeh

Question

The probability that interest rates on housing loans will go up in the next 6 months is estimated to be 0.20. The probability that house sales will decrease is estimated to be 0.6. The probability that interest rates will go up and house sales will decrease is estimated to be 0.15. The probability that interest rates increase and house sales decrease is:

Select one:

a. 0.15

b. 0.71

c. 0.75

d. 0.85

Answer 1

Let A be the event that house sales will decreases in the next 6 months and

B be the event that interest on housing loans will increase in the next 6 months

$P(A) = 0.6 \\ P(B) = 0.20\\ \\ P(A\cap B) = 0.15$

The probability that interest rates increase and house sales decrease is:

$P(A\cap B)$ is 0.15

Hence option (a) is correct.