Question

A box contains 16 batteries of which 7 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.

Answer 1

Answer:

94.71% probability that at least one of the first four works.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the batteries are chosen is not important. So we use the combinations formula solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Either none of the first four does, or at least one does.

The sum of these probabilities is 100%.

Probability none work:

Desired outcomes:

4 batteries from a set of 9 not working. So

$D = C_{9,4} = \frac{9!}{4!5!} = 126$

Total outcomes:

4 batteries from a set of 17

$D = C_{17,4} = \frac{17!}{4!13!} = 2380$

Probability:

[tex]P = \frac{D}{T} = \frac{126}{2380} = 0.0529

5.29% probability that none of the first four work.

Find the probability that at least one of the first four works.

p + 5.29 = 100

p = 94.71

94.71% probability that at least one of the first four works.