Answer :

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

n(S) = ^{52}C_{2}

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 ^{26}C_{2} ways

∴ n(B) = ^{26}C_{2}

∴ 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 ^{4}C_{2} ways

∴ n(K) = ^{4}C_{2}

∴ 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 ^{2}C_{2} ways = 1

∴ P(B ∩ K) =

∴ P(B ∪ K) =

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