Question

In a study conducted for the State Department of Education, 30% of the teachers who left teaching did so because they were laid off. Assume that we randomly select 10 teachers who have recently left their profession. Find the probability that exactly 4 of them were laid off.

A. .2001
B. .2668
C. .3000
D. .0090

Answer 1

A. .2001

Explanation:

For each teacher in the survey, there are only two possible outcomes. Either they were laid off, or they were not. 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.

`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.

In this problem we have that:

30% of the teachers who left teaching did so because they were laid off. This means that
`p = 0.3`

Assume that we randomly select 10 teachers who have recently left their profession. Find the probability that exactly 4 of them were laid off.

This is
`P(X = 4)` when
`n = 10`. So

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

`P(X = 4) = C_(10,4).(0.3)^(4).(0.7)^(6) = 0.2001`

So the correct answer is:

A. .2001