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  • Five cards are drawn successively with replacement from a well -shuffled deck of 52 cards. What is the probability that (iii) none is a spade?

Q. 4  Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that

             (iii) none is a spade?

Answers (1)

best_answer

Let X represent number of spade cards among five drawn cards. Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards.

We have 13 spades .

        P=\frac{13}{52}=\frac{1}{4}

        q=1-P=1-\frac{1}{4}=\frac{3}{4}

X has a binomial distribution,n=5.

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

                P(X=x)=^5C_x.(\frac{3}{4})^{5-x} . (\frac{1}{4})^{x}

             Put X=0 ,

                   P(X=0)=^5C_0.(\frac{3}{4})^{5} . (\frac{1}{4})^{0}

                                          =1\times \frac{243}{1024}

                                         = \frac{243}{1024}                

Posted by

seema garhwal

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