Question

In a certain college, 33% of the physics majors belong to ethnic minorities. find the probability that, from a random sample of 10 physics majors, exactly 4 do not belong to an ethnic minority.

Answer 1

If a random student has a 33% probability of belonging to a minority, then there is a 67% chance that they do not. In a sample of 10 students, the probability that exactly 4 do not belong to a minority is

`\dbinom{10}40.67^4(1-0.67)^(10-4)\approx0.0547`