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  • Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (ii) only 3 cards are spades?

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

             (ii) only 3 cards are spades?

Answers (1)

best_answer

Let X represent a 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=3 ,

                   P(X=3)=^5C_3.(\frac{3}{4})^{2} . (\frac{1}{4})^{3}

                                          =10\times \frac{9}{16}\times \frac{1}{64}

                                         =\frac{45}{512}                

Posted by

seema garhwal

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