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

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

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

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

Correct Answer: 1/2

Explanation:

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

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