Methedologies

Analytical tools assignment 3

Nikhil Nuthakki

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. (7 pts.)

Probability of house sales increase P (A) = 0.25

Probability of interest rates increase P (B) =0.74

Probability of house sales or interest rates increase P (AuB) =0.89

So Probability of both house sales and interest rates increase is

P (A & B) = P (A) + P (B) - P (A or B) = 0.25+0.74-0.89 = 0.1

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. (7 pts.)

In this case we have to find probability of both events doesn’t happen.

Neither event A nor B

Neither A nor B = not (A or B)

P (A or B)' = 1 - P(A or B)

= 1-0.89

= 0.11

So the probability of neither house sales nor interest rates will increase during next six months is 0.11.

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. (6 pts.)

In this case we have to find the probability of only house sales will increase during the next six months.

P(A & B) = P(A) + P(B) - P(A U B) = 0.25+0.74-0.89 = 0.1

P(only A) = P(A) - P(A & B) = 0.25 - 0.1 = 0.15

So the probability of only house sales will increase during next six months is 0.15.

Question 2.

An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend...