A dice is thrown two times. If getting an odd | vedclass

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(D) Let $p$ be the probability of getting an odd number in a single throw of a dice.The possible outcomes on a dice are $\{1, 2, 3, 4, 5, 6\}$.The odd

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(D) Let $p$ be the probability of getting an odd number in a single throw of a dice.The possible outcomes on a dice are $\{1, 2, 3, 4, 5, 6\}$.The odd numbers are $\{1, 3, 5\}$.So,$p = \frac{3}{6} = \frac{1}{2}$.The probability of failure $q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}$.Since the dice is thrown $n = 2$ times,we use the binomial distribution formula $P(X = k) = {}^nC_k p^k q^{n-k}$.For two successes,$k = 2$.$P(X = 2) = {}^2C_2 \left(\frac{1}{2}ight)^2 \left(\frac{1}{2}ight)^{2-2} = 1 	imes \frac{1}{4} 	imes 1 = \frac{1}{4}$.

$A$ dice is thrown two times. If getting an odd number is considered a success,then the probability of two successes is

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