A dice is thrown 5 times,then the probability | vedclass

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(A) The probability of getting an even number in a single throw of a dice is $p = \frac{3}{6} = \frac{1}{2}$.The probability of not getting an even nu

Vedclass · Accepted Answer

$\frac{5}{16}$

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(A) The probability of getting an even number in a single throw of a dice is $p = \frac{3}{6} = \frac{1}{2}$.The probability of not getting an even number is $q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}$.Using the Binomial distribution formula $P(X = r) = {}^nC_r \cdot p^r \cdot q^{n-r}$,where $n = 5$ and $r = 3$:$P(X = 3) = {}^5C_3 \cdot \left(\frac{1}{2}\right)^3 \cdot \left(\frac{1}{2}\right)^{5-3}$$P(X = 3) = 10 \cdot \left(\frac{1}{8}\right) \cdot \left(\frac{1}{4}\right)$$P(X = 3) = \frac{10}{32} = \frac{5}{16}$.

$A$ dice is thrown $5$ times,then the probability that an even number will come up exactly $3$ times is

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