Question

52% of students in a class have brown hair. If 4 students are chosen at random, what is the probability that exactly 3 have brown hair? Write your answer in percent rounded to the nearest whole number.​

Answer 1

`P(X=3)\approx27\%`

Explanation:

Use the binomial distribution

`\displaystyle P(X=k)=\binom{n}{k}p^k(1-p)^(n-k)\\\\P(X=3)=\binom{4}{3}(0.52)^3(1-0.52)^(4-3)\\\\P(X=3)=(4!)/(3!(4-3)!)(0.52)^3(0.48)^1\\ \\P(X=3)=0.26996736\\\\P(X=3)\approx0.27\\\\P(X=3)\approx27\%`

Therefore, the probability that exactly 3 students out of 4 randomly chosen students have brown hair is about 27%