Answer:
P(4) =p(x=4) = 0.205078
Step-by-step explanation:
Explanation:-
The probability of x successes in the n independent trials of the experiment.
Given n=10, p=0.5,
By using Binomial distribution
[tex]P(X =x) = n_{C_{x} } p^{x} q^{n-x}[/tex]
Given the p = 0.5
q=1-p =1-0.5=0.5
[tex]P(X =4) = 10_{C_{4} } (0.5)^{4} (0.5)^{10-4}[/tex]
we will use formula
[tex]n_{C_{r} } = \frac{n!}{(n-r)!r!}[/tex]
[tex]10_{C_{4} } = \frac{10!}{(10-4)!4!}=\frac{10X9X8X7X6!}{6!4!} =\frac{10X9X8X7}{4X3X2X1} =210[/tex]
[tex]P(X =4) = 210 (0.5)^{4} (0.5)^{10-4}[/tex]
[tex]P(X =4) = 210 (0.5)^{4} (0.5)^{6}[/tex]
on calculation, we get
P(X=4) = 0.205078
