SOLUTION: Question 1. 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

Algebra ->  Probability-and-statistics -> SOLUTION: Question 1. 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      Log On


   

Question 1027595: Question 1. 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.
a) What is the probability that both house sales and interest rates will increase during the next 6 months? Show or explain how you obtain your answer.









b) What is the probability that neither house sales nor interest rates will increase during the next 6 months? Show or explain how you obtain your answer.









c) What is the probability that house sales will increase but interest rates will not during the next 6 months? Show or explain how you obtain your answer.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
P(house)+P(interest)-P(both)=probability of P(H OR I). Both subtracts the double counting.
0.25+0.74-P(Both)=0.89
P(BOTH)=0.10
P(neither) is the complement of P(either), which is OR. That is 1-0.89=0.11
If I can assume independence, which probably is not correct since the two are related, it is P(H)*P(not I)=0.25*0.26=0.065. Not I is 1-P(I)=0.26