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.
