A coin is tossed `2n` times. The chance that the number of times one gets head is not equal to the number of times one gets tails is `((2n !))/((n !)^2)(1/2)^(2n)` b. `1-((2n !))/((n !)^2)` c. `1-((2n !))/((n !)^2)1/(4^n)^` d. none of these

Options

A. `.^(2n)C_(n)((1)/(2))^(2n)`
B. `1-.^(2n)C_(n)`
C. `1-.^(2n)C_(n)((1)/(4^n))`
D. none of these

Answer

C

Explanation

Required Probability
`=1-` Probability of getting equal number of heads and tails
`=1-` Probability of getting n heads and n tails
`=1-.^2nC_(n)((1)/(2))^n((1)/(2))^(2n-n)=1-.^2nC_(n)((1)/(4^n))`.