You need to use the binomial probability formula:
[tex]p(k) = \frac{n!}{k!(n-k)!} p^{k} (1-p)^{n-k} [/tex]
where:
n = total number of events = 10
k = number of events we are testing = 6
p = probability of event happening = 0.5
[tex]p(6) = \frac{10!}{6!(10-6)!} 0.5^{6} (1-0.5)^{10-6}[/tex]
= 210×0.015625×0.0625
= 0.205078
Hence, the probability of getting 6 boys out of 10 births is p = 0.205.
