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Mathematics Question on Probability

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?

Answer

S={0,1,2,3,4,5,6,7,8,9} ⇒\Rightarrow n(S)=10

Let A represent that the ball is marked with the digit 0.

∴A={0} ⇒\Rightarrow n(A)=1

P=n(A)n(S)=110  and q=1−p=1−110=910P=\frac{n(A)}{n(S)}=\frac{1}{10} \;and \, q=1-p=1-\frac{1}{10}=\frac{9}{10}

n=4,r=0 and P(X=r)= nCrprqn−r^nC_rp^rq^{n-r}
Now P(one is marked with its digit 0)=4C0(110)0(910)4=656110000^4C_0\bigg(\frac{1}{10}\bigg)^0\bigg(\frac{9}{10}\bigg)^4=\frac{6561}{10000}