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  • 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,

Q. 6  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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Let X denote a number of balls  marked with digit 0 among 4 balls drawn.

Balls are drawn with replacement.

X has a binomial distribution,n=4.

                   P=\frac{1}{10}

                   q=1-P=1-\frac{1}{10}=\frac{9}{10}

                 \therefore \, \, \, \, P(X=x)=^nC_x.q^{n-x}.p^x

                         P(X=x)=^4C_x.(\frac{9}{10})^{4-x} . (\frac{1}{10})^{x}

                 Put  X = 0,

                  P(X=0)=^4C_0.(\frac{9}{10})^{4} . (\frac{1}{10})^{0}

                                       = 1.(\frac{9}{10})^{4}

                                       = (\frac{9}{10})^4

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seema garhwal

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