Answer:
The probability of 4 successes,
P(X=4) =0.0660
Step-by-step explanation:
Step 1:-
Let X be a binomial random variable with n = 9 and p = 0.2
probability of successes p = 0.2
probability of failure q = 1-p = 1-0.2 = 0.8
By using binomial distribution
[tex]P(X=r) = n_{Cr} p^{r} q^{n-r}[/tex]
Step 2:-
The probability of 4 successes, i.e.,
[tex]P(X=4) = 9_{C4} (0.2)^{4} (0.8)^{9-4}[/tex]
by using [tex]n_{Cr} = \frac{n!}{(n-r)!r!}[/tex]
[tex]9_{C4} = \frac{9!}{(9-4)!4!} = \frac{9X8X7X6X5!}{5!4!}[/tex] [tex]= \frac{9X8X7X6}{4!} = \frac{9X8X7X6}{4X3X2X1} =126[/tex]
[tex]P(X=4) =126 X (0.0016)(0.32768)[/tex]
P(X=4) =0.0660
conclusion:-
The probability of 4 successes, that is P(X=4) =0.0660
