Question

In a certain college, 33% of the physics majors belong to ethnic minorities. Of 8 students are selected at random from the physics majors, what is the probability that more than 5 belong to an ethnic minority?

Answer 1

Answer: 0.0187

Explanation:

The binomial distribution formula for probability :-

`P(x)=^nC_xp^x(1-p)^(n-x)`, where P(x) is the probability of getting success in x trials , n is the total number of trials and p is the probability of getting success in each trial.

Given : The probability that the physics majors belong to ethnic minorities =0.33

Number of students selected : n= 8

Now, the probability that more than 5 belong to an ethnic minority :-

`P(x>5)=P(6)+P(7)+P(8)\\\\=^8C_6(0.33)^6(0.67)^(2)+^8C_7(0.33)^7(0.67)^(1)+^8C_8(0.33)^8(0.67)^(0)\\\\=((8!)/(6!2!))(0.33)^6(0.67)^(2)+(8)(0.33)^7(0.67)^(1)+(0.33)^8(0.67)^(0)\\\\=0.0186577086013\approx0.0187`

Hence, the probability that more than 5 belong to an ethnic minority = 0.0187