Q. 203.7( 3 Votes )

Two cards are dra

Answer :

As 2 cards are drawn from a deck of 52 cards. This can be done in 52C2 ways. If S represents the sample space,


n(S) = 52C2


Let B represents the event that both drawn cards are black.


A deck of 52 cards has 26 black cards. So 2 cards can be selected out of those 26 in 26C2 ways


n(B) = 26C2


P(B) =


Let K represents the event that both drawn cards are king.


A deck of 52 cards has 4 king cards. So 2 cards can be selected out of those 4 in 4C2 ways


n(K) = 4C2


P(K) =


We need to find the probability that either both are black or both are kings i.e. P(B or K) = P(B K)


Note: By definition of P(A or B) under axiomatic approach(also called addition theorem) we know that:


P(A B) = P(A) + P(B) – P(A B)


P(B K) = P(B) + P(K) – P(B K)


As we don’t have value of P(B K) so we will find it first.


As there is a common element among the events B and K as both the cards can be a king and can be black 2.


2 black king cards are present so we need to select 2 cards oout of them only. This can be done in 2C2 ways = 1


P(B K) =


P(B K) =


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