A fair coin is tossed 15 times. The probabili | vedclass

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(B) The probability of getting $k$ successes in $n$ trials is given by the binomial distribution formula $P(X=r) = {}^{n}C_r p^r q^{n-r}$.Here,$n=15$,

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$1-\frac{121}{2^{15}}$

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(B) The probability of getting $k$ successes in $n$ trials is given by the binomial distribution formula $P(X=r) = {}^{n}C_r p^r q^{n-r}$.Here,$n=15$,$p=1/2$ (probability of tail),and $q=1/2$ (probability of head).We need to find the probability of getting at least $3$ tails,i.e.,$P(X \geq 3)$.This can be calculated as $P(X \geq 3) = 1 - [P(X=0) + P(X=1) + P(X=2)]$.$P(X=0) = {}^{15}C_0 (1/2)^0 (1/2)^{15} = 1 	imes (1/2)^{15} = 1/2^{15}$.$P(X=1) = {}^{15}C_1 (1/2)^1 (1/2)^{14} = 15 	imes (1/2)^{15} = 15/2^{15}$.$P(X=2) = {}^{15}C_2 (1/2)^2 (1/2)^{13} = \frac{15 	imes 14}{2} 	imes (1/2)^{15} = 105/2^{15}$.Summing these probabilities: $P(X Therefore,$P(X \geq 3) = 1 - \frac{121}{2^{15}}$.

$A$ fair coin is tossed $15$ times. The probability that the tail will appear at least thrice is

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