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.​

Respuesta :

Answer:

[tex]P(X=3)\approx27\%[/tex]

Step-by-step explanation:

Use the binomial distribution

[tex]\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)=\frac{4!}{3!(4-3)!}(0.52)^3(0.48)^1\\ \\P(X=3)=0.26996736\\\\P(X=3)\approx0.27\\\\P(X=3)\approx27\%[/tex]

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