Answer:
0.341 is the probability that the sample contains 1 or more rotten oranges.
Step-by-step explanation:
We are given the following information:
We treat rotten as a success.
Number of oranges = 75
Number of rotten orange = 6
P(Rotten orange) =
[tex]=\dfrac{6}{75} = 0.08[/tex]
Then the number of rotten oranges follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
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:
[tex]P(x \geq 1) =1 - P(x = 0)\\\\=1- \binom{5}{0}(0.08)^0(1-0.08)^5\\\\= 1 - 0.659\\= 0.341[/tex]
0.341 is the probability that the sample contains 1 or more rotten oranges.