Three cards are drawn in succession from a deck without replacement. find the probability distribution for the number of spades
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Hey!
Let the random variable X be the number of spades.
As we want to calculate Pr(X=0), Pr(X=1), Pr(X=2), and Pr(X=3).
Hence, we calculate Pr(X=2).
There are (523) three-card hands, all equally likely. We count the number of two-spade hands.
So, The 2 spades can be chosen in (132) ways. For each of these ways, there are (391) ways to choose the non-spade, for a total of (132)(391).
Thus Pr(X=2)=(132)(391)(523).
Thanks!
-TeamBrainly
(BrainlyManager)
Let the random variable X be the number of spades.
As we want to calculate Pr(X=0), Pr(X=1), Pr(X=2), and Pr(X=3).
Hence, we calculate Pr(X=2).
There are (523) three-card hands, all equally likely. We count the number of two-spade hands.
So, The 2 spades can be chosen in (132) ways. For each of these ways, there are (391) ways to choose the non-spade, for a total of (132)(391).
Thus Pr(X=2)=(132)(391)(523).
Thanks!
-TeamBrainly
(BrainlyManager)
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