A fair coin is tossed 100 times. The probabil | vedclass

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(A) The total number of possible outcomes when a coin is tossed $100$ times is $2^{100}$.The number of ways to get tails an odd number of times is giv

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$\frac{1}{2}$

Vedclass · Answer

(A) The total number of possible outcomes when a coin is tossed $100$ times is $2^{100}$.The number of ways to get tails an odd number of times is given by the sum of combinations: ${}^{100}C_1 + {}^{100}C_3 + {}^{100}C_5 + \dots + {}^{100}C_{99}$.Using the binomial identity,the sum of odd-indexed binomial coefficients is ${}^{n}C_1 + {}^{n}C_3 + \dots = 2^{n-1}$.For $n = 100$,the number of favourable outcomes is $2^{100-1} = 2^{99}$.Therefore,the required probability is $\frac{2^{99}}{2^{100}} = \frac{1}{2}$.

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

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