A box contains 16 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 she has to pick 5 batteries in order to find one that works.
A)0.007
B)0.058
C)0.001
D)12.360
E)0.029

Question

Quizplus · Accepted Answer

The probability of picking a working battery on any given trial is 6/16 (or 3/8). The probability of not picking a working battery on any given trial is 10/16 (or 5/8).

To find the probability of picking 5 batteries before finding one that works, we need to find the probability of not finding a working battery on the first 4 tries (since we know the 5th battery will be the one that works) and then finding a working battery on the 5th try.

So, the probability of not finding a working battery on each of the first 4 tries is (5/8) * (5/8) * (5/8) * (5/8) = 625/4096. The probability of finding a working battery on the 5th try is 6/16 (or 3/8).

Therefore, the overall probability is: 
(5/8) * (5/8) * (5/8) * (5/8) * (3/8) = 375/32768

Simplifying: 
375/32768 ≈ 0.0576

So the best choice is B) 0.058.

A Box Contains 16 Batteries of Which 6 Are Still