A fair coin is tossed 100 times. The probability of getting tails an odd number of times is

Step-by-step solution

Probability of getting a tail in a single toss p= 1 2 and not getting tail, q= 1 2 . Using Binomial distribution, Required probability aligned & =P(X=1)+P(X=3)+P(X=5)+ & +P(X=99) & = ¹⁰⁰ C₁ ( 1 2 )^1 ( 1 2 )⁹⁹+ ¹⁰⁰ C₃ ( 1 2 )^3 ( 1 2 )⁹⁷ & + ¹⁰⁰ C₅ ( 1 2 )^5 ( 1 2 )⁹⁵+ .+ 100 99 ( 1 2 )⁹⁹ ( 1 2 ) & = ( 1 2 )¹⁰⁰ ( ¹⁰⁰ C₁+ ¹⁰⁰ C₃+ ¹⁰⁰ C₅+ + 100 99 ) & = 1 2²⁰⁰ (2⁹⁹ ) & = 1 2 & aligned