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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$1/2$

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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 given by the sum of combinations: $\binom{100}{1} + \binom{100}{3} + \dots + \binom{100}{99}$.Using the binomial identity $\sum_{k 	ext{ odd}} \binom{n}{k} = 2^{n-1}$,we have $\binom{100}{1} + \binom{100}{3} + \dots + \binom{100}{99} = 2^{100-1} = 2^{99}$.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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