Question

Harrison Water Sports has two retail outlets: Seattle and Portland. The Seattle store does 60 percent of the total sales in a year. Further analysis indicates that if a sale is made in Seattle, there is 0.40 probability this is a sale of boat accessories, while if a sale is made at the Portland store this probability is 0.20. If Harrison Water Sports knows that a boat accessory has been sold, what is the probability this sale has occurred in Seattle:

	a.	0.24
	b.	2/3
	c.	3/4
	d.	None of the above

Answer 1

We use Bayes Theorem

Let S and P denote the events of sale in Seattle and Portland.

Let B denote a sale of boat accessory.

Given,

P(S) = 60% = 0.6

P(P) = 1- 0.6 = 0.4

P(B/S) = 0.4

P(B/P) = 0.2

$P(S | B) = \frac{P(S)*P(B|S)}{P(P)*P(B|P) + P(S)*P(B|S)}$

$= \frac{0.6*0.4}{0.4*0.2 + 0.6*0.4} = 3/4 = 0.75$

Ans is c) 3/4