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 probability that both house sales and interest rates will increase during the next 6 months is ________. question 2 options: 1) 0.705 2) 0.10

Answer 1

Recall that given two events A and B, then P(A or B) = P(A) + P(B) - P(A and B)

Given that 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.

Let the probability that both house sales and interest rates will increase during the next 6 months be x, then

0.89 = 0.74 + 0.25 - x

⇒ x = 0.99 - 0.89 = 0.10

Therefore, the probability that both house sales and interest rates will increase during the next 6 months is 0.10.