A box contains 14 batteries of which 6 are still working.Anne starts picking batteries one at a time from the box and testing them.Find the probability that at least one of the first four works.
A)0.893
B)0.015
C)0.084
D)0.930
E)0.070

Question

Quizplus · Accepted Answer

The probability of picking a working battery on the first try is 6/14. After one working battery is picked, the probability of picking another working battery on the second try is 5/13. Similarly, the probability of picking a working battery on the third and fourth tries, given that two and three working batteries have already been picked, respectively, are 4/12 and 3/11. 
To find the probability of at least one of the first four batteries working, we can find the probability of none of the first four working and subtract from 1. The probability of none of the first four batteries working is (8/14) x (7/13) x (6/12) x (5/11) = 0.132. 
Therefore, the probability of at least one of the first four batteries working is 1 - 0.132 = 0.868, which is closest to choice D, 0.930.

A Box Contains 14 Batteries of Which 6 Are Still