A drug is being tested on lab mice. 80% of mice die when injected and 20% of mice can resist this drug. For his research, a scientist needs 5 resistant mice.

Question

What is the probability that the scientist killed 25 mice till he got 5 resistant mice in total?

Answer 1

This is the negative binomial of 25 failures before the fifth success with probability .2.

In Excel, you can use =NEGBINOM.DIST(25,5,0.2,0)

Alternatively, it is the binomial of 25 failures and 4 successes * the probability of a success =

BINOM.DIST(4,29,0.2,0)*0.2

Of course, the calculation is the same in both of these cases: =Combin(29,4)*.2^5*.8^25

With any of the three calculations, the answer is 0.0287131971416671