There are currently 18 pit bulls at the pound. Of the 18 pit bulls, four have attacked another dog in the last year. Joe, a member of the staff, randomly selects six of the pit bulls for his group. What is the probability that exactly one of the pit bulls in Joe's group attacked another dog last year?
A) 0.1618
B) 0.3235
C) 0.4314
D) 0.4853

Question

Quizplus · Accepted Answer

To find the probability that exactly one of the pit bulls in Joe's group attacked another dog last year, we need to use the binomial distribution. Letting $p$ be the probability that any one of the pit bulls in the pound attacked another dog last year, we have $p=\frac{4}{18}=\frac{2}{9}$. The probability of exactly one success (i.e. one pit bull that attacked another dog) in six trials (i.e. six pit bulls selected for Joe's group) is given by the binomial probability:
$$P(X=1) = \binom{6}{1}p^1(1-p)^5 = 6\left(\frac{2}{9}ight)\left(\frac{7}{9}ight)^5 \approx 0.4314$$
Therefore, the best choice is $\boxed{	extbf{(C)}}$.

There Are Currently 18 Pit Bulls at the Pound