A fair coin is tossed 100 times . The probability of

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

1. 1/2
2. 1/8
3. 3/8
4. None of these

Correct Option: A

The total number of cause is 2¹⁰⁰.
The number of favourable cases are ¹⁰⁰C₁ + ¹⁰⁰C₃ + ..... + ¹⁰⁰C₉₉
= 2^{100 - 1} = 2⁹⁹
∴ Reqd probability = 2⁹⁹/ 2¹⁰⁰ = 1/2