Answer:
The value of given expression is [tex]\frac{21}{128}[/tex].
Step-by-step explanation:
Given information: n=7, x=2, p=1/2
[tex]q=1-p=1-\frac{1}{2}=\frac{1}{2}[/tex]
The given expression is
[tex]C(n,x)p^xq^{n-x}[/tex]
It can be written as
[tex]^nC_xp^xq^{n-x}[/tex]
Substitute n=7, x=2, p=1/2 and q=1/2 in the above formula.
[tex]^7C_2(\frac{1}{2})^2(\frac{1}{2})^{7-2}[/tex]
[tex]\frac{7!}{2!(7-2)!}(\frac{1}{2})^2(\frac{1}{2})^{5}[/tex]
[tex]\frac{7!}{2!5!}(\frac{1}{2})^{2+5}[/tex]
[tex]\frac{7\times 6\times 5!}{2\times 5!}(\frac{1}{2})^{2+5}[/tex]
[tex]21(\frac{1}{2})^{7}[/tex]
[tex]\frac{21}{128}[/tex]
Therefore the value of given expression is [tex]\frac{21}{128}[/tex].
