A die is thrown five times. If getting an odd | vedclass

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(D) Here,$n=5$,$p=\frac{1}{2}$,$q=\frac{1}{2}$.Probability of getting at least $4$ successes is given by $P(X \ge 4) = P(X=4) + P(X=5)$.Using the bino

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$\frac{3}{16}$

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(D) Here,$n=5$,$p=\frac{1}{2}$,$q=\frac{1}{2}$.Probability of getting at least $4$ successes is given by $P(X \ge 4) = P(X=4) + P(X=5)$.Using the binomial distribution formula $P(X=r) = {}^nC_r p^r q^{n-r}$:$P(X=4) = {}^5C_4 \left(\frac{1}{2}ight)^4 \left(\frac{1}{2}ight)^1 = 5 	imes \frac{1}{16} 	imes \frac{1}{2} = \frac{5}{32}$.$P(X=5) = {}^5C_5 \left(\frac{1}{2}ight)^5 \left(\frac{1}{2}ight)^0 = 1 	imes \frac{1}{32} 	imes 1 = \frac{1}{32}$.Therefore,$P(X \ge 4) = \frac{5}{32} + \frac{1}{32} = \frac{6}{32} = \frac{3}{16}$.

$A$ die is thrown five times. If getting an odd number is a success,then the probability of getting at least $4$ successes is

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