Two cards are drawn successively with replacement from a pack of 52 cards. Find the probability distribution of the number of face cards.
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Two cards are drawn successively with replacement from a pack of 52 cards. Find the probability distribution of the number of face cards.
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Answer:
Solution
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Correct option is A)
Total no. of cards = 52
Total no. of aces = 4
P(ace)=
52
4
=
13
1
P(non−ace)=
52
48
=
13
12
Let X be a random variable, such that
X = no. of aces obtained in 2 draws.
Case I:- X = 0 (No aces are obtained)
P(X=0)=P(non-ace and non-ace)
=P(non−ace)×P(non−ace)
=
13
12
×
13
12
=
169
144
Case II:- X = 1 (1 ace is obtained)
P(X=1)=P((ace and non-ace) or (non-ace and ace))
=(P(non−ace)×P(non−ace))+(P(ace)×P(non−ace))
=(
13
12
×
13
1
)+(
13
1
×
13
12
)
=
169
24
Case III:- X = 2 (two aces are obtained)
P(X=2)=P(ace and ace)
=P(ace)×P(ace)
=
13
1
×
13
1
=
1/169
Step-by-step explanation: