Question

It is known that seventy percent (70%) of married couples paid for their honeymoon themselves. You randomly select 9 independent married couples and ask each if they paid for their honeymoon themselves. Let our random variable be X = the number of married couples that paid for their honeymoon themselves. What is the probability that all married coupled asked stated they paid for their honeymoon themselves? (Round your answer to four decimal places).

Answer 1

0.0404 = 4.04% probability that all married coupled asked stated they paid for their honeymoon themselves.

Explanation:

For each couple, there are only two possible outcomes. Either they paid for their honeymoon, or they did not. The probability of a couple having paid for their honeymoon is independent of any other couple, which means that the binomial probability distribution is used 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.

It is known that seventy percent (70%) of married couples paid for their honeymoon themselves.

This means that
`p = 0.7`

You randomly select 9 independent married couples.

This means that
`n = 9`

What is the probability that all married coupled asked stated they paid for their honeymoon themselves?

This is P(X = 9). So

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

`P(X = 9) = C_(9,9).(0.7)^(9).(0.3)^(0) = 0.0404`

0.0404 = 4.04% probability that all married coupled asked stated they paid for their honeymoon themselves.