You flip a coin 10 times. Knowing that the event satisfies the requirements for a binomial distribution, find the probability that exactly 7 of the outcomes are heads.

Assuming a fair coin, and requirements for a binormial distribution are satisfied, then 
p=0.50
n=20
The number of successes, x, is then given by[tex]P(x)=C(n,x)p^x(1-p)^{n-x}[/tex]where[tex]C(n,x)=\frac{n!}{x!(n-x)!}[/tex]
For x=7,
[tex]P(x)=C(n,x)p^x(1-p)^{n-x}[/tex]
[tex]P(7)=C(n,x)p^x(1-p)^{n-x}[/tex]
[tex]=C(20,7)0.5^7(0.5)^{20-7}[/tex]
[tex]=C(20,7)0.5^{20}[/tex]
[tex]=\frac{77520}{1048576}[/tex]
[tex]=\frac{4845}{65536}[/tex]
[tex]=0.07393[/tex]    to 5 places of decimal

Ans. the probability is 0.07393 to 5 places of decimal.