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

Answer:

0.7558 = 75.58% probability this sale has occurred in Dallas

Step-by-step explanation:

Conditional Probability

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

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

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?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.325}{0.43} = 0.7558$

0.7558 = 75.58% probability this sale has occurred in Dallas