A die is thrown 6 times. If 'getting an odd n | vedclass

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Question

(A) The repeated tosses of a die are Bernoulli trials. Let $X$ denote the number of successes of getting odd numbers in an experiment of $n=6$ trials.

Vedclass · Accepted Answer

$\frac{3}{32}$

Vedclass · Answer

(A) The repeated tosses of a die are Bernoulli trials. Let $X$ denote the number of successes of getting odd numbers in an experiment of $n=6$ trials.The probability of getting an odd number in a single throw of a die is $p = \frac{3}{6} = \frac{1}{2}$.Therefore,the probability of failure is $q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}$.$X$ follows a binomial distribution with parameters $n=6$ and $p=\frac{1}{2}$.The probability mass function is given by $P(X=x) = ^{n}C_{x} p^{x} q^{n-x}$.We want to find the probability of $5$ successes,i.e.,$P(X=5)$.$P(X=5) = ^{6}C_{5} \left(\frac{1}{2}ight)^{5} \left(\frac{1}{2}ight)^{6-5}$.$P(X=5) = 6 	imes \left(\frac{1}{2}ight)^{5} 	imes \left(\frac{1}{2}ight)^{1} = 6 	imes \left(\frac{1}{2}ight)^{6}$.$P(X=5) = 6 	imes \frac{1}{64} = \frac{6}{64} = \frac{3}{32}$.

$A$ die is thrown $6$ times. If 'getting an odd number' is a success,what is the probability of $5$ successes?

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