Question

Of police academy applicants, only 25% will pass all the examinations. suppose that 12 successful candidates are needed. what is the probability that, by examining 20 candidates, the academy finds all of the 12 persons needed?

Answer 1

The probability is 0.0008.

I used a binomial probability on this one, since there are two outcomes (either pass or fail); the events are independent (the probability of one person passing does not influence the probability of another passing); and there are a fixed number of trials (in this case, 20).

For binomial probabilities, we use the formula:
$_nC_k=p^k*(1-p)^{n-k}$

With our information, we have: