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

Answer:

$P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972$

Step-by-step 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.

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

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

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

$P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972$