A fair coin is tossed 100 times, The probability of getting

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A fair coin is tossed 100 times, The probability of getting head an odd number of times is ?

1. 1/4
2. 2/3
3. 1/2
4. 3/4

Correct Option: C

n(S) = 2¹⁰⁰
n(E) = No. of favourable ways = ¹⁰⁰C₁ + ¹⁰⁰C₃ + ... ¹⁰⁰ C₉₉ = 2^100-1 = 2⁹⁹
[∵ ⁿC₁ + ⁿC₃ + ⁿC₅ + ........................... = 2^n-1 ]
∴ P(E)= n(E)/n(S) = 2⁹⁹/2¹⁰⁰ = 1/2

Note : The given case can be generalised as "If a unbiased coin is tossed 'n' times, then the chance that the head will present itself an odd number of times is 1/2. "