Answer to Question #185320 in Statistics and Probability for Mariam

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.)

9. An oil prospector will drill a succession of holes in a given area to find a productive well. The

probability that he is successful on a given trial is .2.

(a) What is the probability that the third hole drilled is the first to yield a productive well

Answer 1

1. When there is a defect, you return the amount paid ($100) and double this amount, which means that in total you will lose $100.

The expected total cost of 1 motor is the sum of the products of the gain and their probability:

EV = $100 $\times$ 0.92 + (-$100) $\times$ 0.08 = $84

The expected net gain for the seller on the 10 motors is then:

10 $\times$ $84 = $840

2. p = 0.2

q = 1 – p = 1 – 0.2 = 0.8

Geometric probability:

$p(y) = q^{y-1}p \\ p(3) = 0.8^{3-1}0.2 \\ = 0.128 \\ = 12.8 \%$