Question

Approximately 20% of U.S. workers are afraid that they will never be able to retire. Suppose 10 workers are randomly selected. What is the probability that none of the workers is afraid that they will never be able to retire

Answer 1

Answer:

10.74% probability that none of the workers is afraid that they will never be able to retire

Step-by-step explanation:

For each worker, there are only two possible outcomes. Either they are afraid that they are never going to be able to retire, or they are not. The probability of a worker being afraid that they are never going to be able to retire is independent of other workers. 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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

20% of U.S. workers are afraid that they will never be able to retire.

This means that $p = 0.2$

10 workers

This means that $n = 10$

What is the probability that none of the workers is afraid that they will never be able to retire

This is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

10.74% probability that none of the workers is afraid that they will never be able to retire