Question

It is known that 60% of the students at a large university have a job and 40% do not have a job. If three of these students are randomly selected what is the probability all three have jobs?

a. 0.360
b. 0.216
c. 0.648
d. 0.060

Answer 1

b. 0.216

Explanation:

For each student, there are only two possible outcomes. Either they have a job, or they do not. The probability of a student having a job is independent of other students. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

60% of the students at a large university have a job

This means that
`p = 0.6`

If three of these students are randomly selected what is the probability all three have jobs?

This is
`P(X = 3)` when
`n = 3`. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 3) = C_(3,3).(0.6)^(3).(0.4)^(0) = 0.216`

So the correct answer is:

b. 0.216