Question

Two stores sell a certain product. Store A has 45% of the sales, 3% of which are of defective items, and store B has 55% of the sales, 4% of which are of defective items. The difference in defective rates is due to different levels of pre-sale checking of the product. A person receives one of this product as a gift. What is the probability it is defective

Answer 1

Answer:

$Probability = 0.0355$

Step-by-step explanation:

Given

Stot A:

$Sales = 45\%$

Defective = 3%

Store B

$Sales = 55\%$

Defective = 4%

Required

Determine the probability a product received is defective.

First, we calculate the probability that the defective product is from store A

$Probability = P(Sales) * P(Defective)$

$P_A = 45\% * 3\%$

Convert to decimals

$P_A= 0.45 * 0.03$

$P_A= 0.0135$  

Next, we calculate the probability that the defective product is from store B

$P_B= 55\% * 4\%$

$P_B= 0.55 * 0.04$

$P_B= 0.022$

The product may come from either stores.

So, the probability of having a defective product is:

$Probability = P_A + P_B$

$Probability = 0.0135 + 0.022$

$Probability = 0.0355$