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

Correct Answer: 1/2

Explanation:

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


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