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(A) Let $X$ denote the number of balls marked with the digit $0$ among the $4$ balls drawn.Since the balls are drawn with replacement,the trials are B

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$\left(\frac{9}{10}\right)^{4}$

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(A) Let $X$ denote the number of balls marked with the digit $0$ among the $4$ balls drawn.Since the balls are drawn with replacement,the trials are Bernoulli trials.$X$ follows a binomial distribution with $n=4$ and probability of success $p = \frac{1}{10}$ (drawing a ball marked $0$).The probability of failure is $q = 1 - p = 1 - \frac{1}{10} = \frac{9}{10}$.The probability of $x$ successes is given by $P(X=x) = ^{n}C_{x} \cdot p^{x} \cdot q^{n-x}$.We want the probability that none of the balls is marked with $0$,which is $P(X=0)$.$P(X=0) = ^{4}C_{0} \cdot \left(\frac{1}{10}\right)^{0} \cdot \left(\frac{9}{10}\right)^{4-0}$.$P(X=0) = 1 \cdot 1 \cdot \left(\frac{9}{10}\right)^{4} = \left(\frac{9}{10}\right)^{4}$.

$A$ bag consists of $10$ balls each marked with one of the digits $0$ to $9$. If four balls are drawn successively with replacement from the bag,what is the probability that none is marked with the digit $0$?

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