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 at least one does not have a job? (Hint: the compliment of this event is all three have jobs.)

78.4% probability at least one does not have a job

Step-by-step explanation:

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

Binomial probability distribution

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

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

And p is the probability of X happening.

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

This means that

Three of these students are randomly selected

This means that

What is the probability at least one does not have a job?

Either all of them have a job, or at least one does not. The sum of the probabilities of these events is decimal 1. So

We want P(X < 3). Then

In which

78.4% probability at least one does not have a job

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

replace   with   27   and simplify.

10 , 27 , 10 , 70 , 10 , 35 , 10 , 48

step-by-step explanation: