A dice is thrown 10 times. If getting an even | vedclass

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(D) The probability of getting an even number in a single throw of a dice is $p = \frac{3}{6} = \frac{1}{2}$.Consequently,the probability of failure i

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$^{10}C_6 (\frac{1}{2})^{10}$

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(D) The probability of getting an even number in a single throw of a dice is $p = \frac{3}{6} = \frac{1}{2}$.Consequently,the probability of failure is $q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}$.Using the binomial distribution formula $P(X = r) = ^nC_r p^r q^{n-r}$,where $n = 10$ and $r = 4$:$P(X = 4) = ^{10}C_4 (\frac{1}{2})^4 (\frac{1}{2})^{10-4}$$P(X = 4) = ^{10}C_4 (\frac{1}{2})^4 (\frac{1}{2})^6 = ^{10}C_4 (\frac{1}{2})^{10}$.Since $^{10}C_4 = ^{10}C_{10-4} = ^{10}C_6$,the probability can also be written as $^{10}C_6 (\frac{1}{2})^{10}$.Thus,the correct option is $D$.

$A$ dice is thrown $10$ times. If getting an even number is considered as a success,then the probability of $4$ successes is:

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