An unbiased coin is tossed is tossed a fixed number of times. If the probability of getting 4 heads equals the probability of getting 7 heads, then the probability of getting 2 heads , is

Options

A. `(55)/(2048)`
B. `(3)/(4096)`
C. `(1)/(1024)`
D. None of these

Answer

A

Explanation

Let the coin be tossed n times and let X denotes the number of heads in n tosses . Then ,
`P(X=r)=""^(n)C_(r)(1/2)^(n)`
Now, `P(X=4)=P(X=7)`
`implies ""^(n)C_(4)=""^(n)C_(7)`
`implies n=11" "[therefore ""^(n)C_(x)=""^(n)C_(y)implies x+y=n]`
`therefore P(X=2)=""^(11)C_(2)(1/2)^(11)=(55)/(2048)`