Question

A bag consists of 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?

Answer 1

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 trails.

p=P (balls drawn is marked with 0)= $\frac{1}{10}$

($\because$ only one ball out of 10 is marked with 0)

$\Rightarrow$ q=1 -p=$\frac{9}{10}$

Required probability = P(none marked with 0 )

$\therefore$ P(X=r)= ${}^4{C}_0{p}^0{q}^4=q^4={\left(\frac{9}{10}\right)}^4$