The probability that house sales will increase in the next six 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 six months is estimated to be 0.89.
- The probability that house sales will increase but interest rates will not increase during the next six months is
A) 0.065.
B) 0.51.
C) 0.89.
D) 0.15.

Question

Quizplus · Accepted Answer

Let A be the event that house sales increase in the next six months, and let B be the event that interest rates on housing loans go up in the same period.

We are given:

P(A) = 0.25
P(B) = 0.74
P(A or B) = 0.89

We can use the formula:

P(A and not B) = P(A) - P(A and B)

We know that:

P(A and B) = P(A) + P(B) - P(A or B)
= 0.25 + 0.74 - 0.89 
= 0.10

Therefore,

P(A and not B) = P(A) - P(A and B)
= 0.25 - 0.10 
= 0.15

So the probability that house sales will increase but interest rates will not increase during the next six months is 0.15, which corresponds to answer D.

The Probability That House Sales Will Increase in the Next