Question

The chance of rain on a randomly selected day in Western Oregon between June 21st and September 21st is 30% each day. What is the probability it rains at least 2 out of any randomly selected 5 days during the given time of year? (round your answer to the nearest hundredth)

Answer 1

0.47 is the probability it rains at least 2 out of any randomly selected 5 days during the given time of year

Explanation:

We are given the following information:

We treat training as a success.

P(Rain) = 30% = 0.30

Then the chances of rain on each day follows a binomial distribution, where

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 5

We have to evaluate:

`P(x \geq 2) =1- P(x = 0) + P(x = 1) \\=1- \binom{5}{0}(0.3)^0(1-0.3)^5 - \binom{5}{1}(0.3)^1(1-0.3)^4\\=1- 0.16807- 0.36015\\= 0.47178 \approx 0.47`

0.47 is the probability it rains at least 2 out of any randomly selected 5 days during the given time of year