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 neither house sales nor interest rates will increase during the next 6 months is _______.

Answer 1

0.11

Explanation:

Probability that house sale will increase = P(A) = 0.25

Probability that interest rate on house loans will go up = P(B) = 0.74

Probability that either house sales will go up or interest rates will go up = P(A or B ) = 0.89

We have to find the probability that neither house sales nor interest rates will increase. This event is the compliment of the event that either house sales will go up or interest rates will go up.

i.e.

Probability that neither house sales nor interest rates will increase =
`P(A \cup B)^(c)`

`P(A\cup B)^(c) = 1 - P(A \cup B)`

Using the value of P(A U B), we get:

`P(A\cup B)^(c) = 1 - 0.89\\\\ P(A\cup B)^(c) = 0.11`

The probability that neither house sales nor interest rates will increase during the next 6 months is 0.11