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Three cards are drawn successively with replacement from a well shuffled deck of 52 playing cards. If getting a card of spade is considered a success, find the probability distribution of the number of success.

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  • Once we write down the sample space for the problem we can find the favorable outcomes in each case and find their probabilities and arrange as a probability distribution.
Step 1:
Let $X$ denote the no of spade cards in three draws.
$\therefore x$ can take values 0,1,2,3
$P(X=0)$=Probability of not getting a spade card.
Probability of getting a spade card is $P(S)=\large\frac{13}{52}$
$\Rightarrow \large\frac{1}{4}$
Probability of not getting a spade card is $P(F)=1-\large\frac{1}{4}$
$\Rightarrow \large\frac{3}{4}$
Step 2:
Step 3:
Hence the required probability is
answered Oct 2, 2013 by sreemathi.v

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