Question

You have 10 batteries sitting on your desk, three of which are dead. You choose 2 batteries are random for you calculator. What is the expected number of good batteries that you get?

A) 0

B) 1

C) 1.4

D) 2

Answer 1

C) 1.4

Explanation:

The probability of choosing 2 good ones is 7/10·6/9 = 42/90.

The probability of choosing 1 good one is 7/10·3/9 +3/10·7/9 = 42/90.

The probability of choosing 0 good ones is 3/10·2/9 = 6/90

The expected value is the sum of the product of number of good ones and their probability:

... 2·42/90 +1·42/90 +0·6/90 = (2+1)·42/90 = 42/30 = 1.4