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?

.: The probability of ball with digit 0 is drawn $= \cfrac{1}{{10}}$

let $p$ be the probability of success $= \cfrac{1}{{10}}$

$X$ has the binomial distribution with $n = 4,p = \cfrac{1}{{10}},q = \cfrac{9}{{10}}$

$\therefore P(X = r){ = ^n}{C_r}{(q)^{n - r}}{p^r}$

$\therefore P$ (none is marked with 0 ) $= P(X = 0)$

${ = ^4}{C_0}{q^4}{p^0} = (1){\left( {\cfrac{9}{{10}}} \right)^4}(1) = {\left( {\cfrac{9}{{10}}} \right)^4}$