Q:

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?

Accepted Solution

A:
Answer: 0.0187Step-by-step explanation:The binomial distribution formula for probability :-[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], 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 =0.33Number of students selected : n= 8Now, the probability that more than 5 belong to an ethnic minority :-[tex]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}\\\\=(\dfrac{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[/tex]Hence, the probability that more than 5 belong to an ethnic minority = 0.0187