A fair coin is tossed 100 times. The probability of getting a head for even number of times is

Step-by-step solution

We have n=100 and probability of getting head =1 / 2 Let p =1 / 2 q =1 / 2 Probability of getting head even number of times = aligned & P ( X =2)+( X =4)+ . .+( X =100)] & = [ ¹⁰⁰ C ₂ ( 1 2 )^2 ( 1 2 )⁹⁸+ .+ ¹⁰⁰ C ₁₀₀ ( 1 2 )¹⁰⁰ ( 1 2 )^ ] & = ( 1 2 )¹⁰⁰ [ ¹⁰⁰ C ₂+ ¹⁰⁰ C ₄+ .+ ¹⁰⁰ C ₁₀₀ ] & = ( 1 2 )¹⁰⁰ [2¹⁰⁰⁻¹ ]= 1 (2)¹⁰⁰ (2)⁹⁹= 1 2 aligned