Question

A scientist inoculates several mice, one at a time, with a disease germ until he finds 3 mice that have attacked by the disease. If the probability of getting attack of the disease is 1/5, what is the probability that 10 mice are required

Answer 1

Apply the Negative Binomial distribution.

Let $n=10$ be the sample size of the sample until we get $r=3$ successes. The probability of contracting the disease is $p=1/5.$. The form of the Negative Binomial distribution we apply is given as,

$$p(X=n)=\binom{n-1}{r-1}p^r(1-p)^{n-r}$$

.Therefore,

$$p(X=10)=\binom{10-1}{3-1}(\dfrac{1}{5})^3(1-\dfrac{1}{5})^{10-3}$$

$$=36(0.008)(0.2097152)=0.0603979776$$