Question

Q13. Mavi Jeans has two retail outlets: Dallas and Phoenix. The Dallas store does 65 percent of the total sales in a year. Further analysis indicates that if a sale is made in Dallas, there is 0.5 probability this is a sale of belts, while if a sale is made at the Phoenix store this probability is 0.3. If Mavi Jeans knows that a belt has been sold, what is the probability this sale has occurred in Dallas

Answer 1

0.7558 = 75.58% probability this sale has occurred in Dallas

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Belt sold

Event B: Sold in Dallas.

Probability of belt being sold:

50% of 65%(made in Dallas)

30% of 100 - 65 = 35%(made in Phoenix). So

`P(A) = 0.5*0.65 + 0.3*0.35 = 0.43`

Sold in Dallas:

50% of 65%. So

`P(A \cap B) = 0.5*0.65 = 0.325`

What is the probability this sale has occurred in Dallas?

`P(B|A) = (P(A \cap B))/(P(A)) = (0.325)/(0.43) = 0.7558`

0.7558 = 75.58% probability this sale has occurred in Dallas