Question

in a certain college 33% of the physics majors belong to ethnic minorities. if 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

We need the sum of probabilities of 6, 7 and 8

This is much more advanced than your previous questions and requires use of the binomial distribution rules.

P(x=k) = C(n,k) p^k p^(n-k)
where C(n,k)=n!/[k!(n-k)!]

so for example the P(x=6) is
P(x=6)= C(8,6) .33^6 * .67^2
where C(8,6) = 8!/[6!*2!]=28
so
P(x=6) = 28* .33^6 * .67^2
= 0.01623

now do that for P(x=7)
and for P(x=8)

and add the three results.