Answer to Question #323804 in Statistics and Probability for Bless

Question

Ten motors are packaged for sale in a certain warehouse. The motors sell for $100 each, but a double-your-money-back guarantee is in effect for any defectives the purchaser may receive. Find the expected net gain for the seller if the probability of any one motor being defective is .08. (Assume that the quality of any one motor is independent of that of the others.)

Answer 1

Let X - the seller's net gain from the sale of one motor. It may be $100 or - $200.

The probabilities of these values are:

$P(X=100)=1-0.08=0.92,\\ P(X=-200)=0.08.$

The expected net gain from the sale of one motor:

$\mu=\sum x_i\cdot P(X=x_i)=\\ =100\cdot0.92-200\cdot0. 08=76.$

The total expected net gain from the sale of ten motors:

$76\cdot 10=\$760.$