Answer:
P(x = 0) = 0.004
P(x = 0) = 0.047
P(x = 0) = 0.211
P(x = 0) = 0.422
P(x = 0) = 0.316
Step-by-step explanation:
We are given the following information:
We treat a person who does not become a repeat offender as a success.
P(Success) = P(person who does not become a repeat offender) = 0.75
Then the number of people 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 = 4
We have to evaluate:
[tex]P(x = 0)\\= \binom{4}{0}(0.75)^0(1-0.75)^4 = 0.004[/tex]
[tex]P(x = 1)\\= \binom{4}{1}(0.75)^1(1-0.75)^3 = 0.047[/tex]
[tex]P(x = 2)\\= \binom{4}{2}(0.75)^2(1-0.75)^2 = 0.211[/tex]
[tex]P(x = 3)\\= \binom{4}{3}(0.75)^3(1-0.75)^1 = 0.422[/tex]
[tex]P(x = 4)\\= \binom{4}{4}(0.75)^4(1-0.75)^0 = 0.316[/tex]
