Answer to Question #260653 in Statistics and Probability for Gab

Question

A paint-store chain produces and sells latex and semigloss paint. Based on long-range sales, the probability that a customer will purchase latex paint is 0.75. Of those that purchase latex paint, 60% also purchase rollers. But only 30% of semigloss paint buyers purchase rollers. A randomly selected buyer purchases a roller and a can of paint. What is the probability that the paint is latex?

Answer 1

A paint store chain produces and sells Latex ad semigloss paint.

Let L & S denote the events that the customer has purchased latex paint or semigloos paint respectively.

P(L) =0.75

P(S) = 1-P(L)

= 1- 0.75

= 0.25

Also, Suppose R be the event which denotes that customer has purchased a roller.

$P(R | L) =0.6 \\ P(R | S) = 0.30 \\ P(L | R) = \frac{P(R| L) \times P (L) }{ P(R| L) \times P(L) +P(R |S) \times P(S)} \\ = \frac{0.6 \times 0.75 }{ (0.6 \times 0.75)+(0.3 \times 0.25)} \\ =\frac{0.45}{0.525} \\ =0.857$