NCERT Class XII Mathematics Chapter - - Solutions
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Question : 71
Total: 101
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) none is a spade?
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) none is a spade?
Solution:
Let p be the probability of drawn card is spade =
=
∴ q = 1 −
=
X has a binomial distribution withn = 5 , p =
, q =
⇒ P ( X = r ) = n C r q n − r p r
(i) P (all five cards are spades) = P(X = 5)
= 5 C 5 q 0 p 5 = 1 × 1 × (
) 5 =
(ii) P (only 3 cards are spades) = P(X = 3)
= 5 C 3 q 2 p 3 = 10 × (
) 2 × (
) 3 =
(iii) P (none is a spade) = P(X = 0)= 5 C 0 q 5 p 0 = 1 × (
) 5 × 1 =
X has a binomial distribution with
(i) P (all five cards are spades) = P(X = 5)
(ii) P (only 3 cards are spades) = P(X = 3)
(iii) P (none is a spade) = P(X = 0)
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