Question

the hiking club plans to go camping In a state park where the probability of rain on any given day is 0.7. which expression can be used to find the probability that it will rain on exactly 3 of the seven days they are there

Answer 1

`P(X = 3) = C_(7,3).(0.7)^(3).(0.3)^(4) = 0.0972`

Explanation:

For each day there are only two possible outcomes. Either it rains, or it does not. The probability of rain on a day is independent of any other day. 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 a state park where the probability of rain on any given day is 0.7.

This means that
`p = 0.7`

Which expression can be used to find the probability that it will rain on exactly 3 of the seven days they are there

We have to find
`P(X = 3)` when
`n = 7`

So

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

`P(X = 3) = C_(7,3).(0.7)^(3).(0.3)^(4) = 0.0972`