From a well shuffled deck of 52 cards, 4 cards are drawn at random. What is the probability that all the drawn cards are of the same colour.

In a deck of 52 cards there are 2 colours. Each colour having 26 cards.


As we need to choose 4 cards out of 52. Let S represents the sample space.


n(S) = 52C4


Let A represents the event that all 4 cards drawn are black.


n(A) = ways in which 4 cards can be selected from 26 black cards.


n(A) = 26C4


P(A) = 26C4/52C4 =


Let B represents the event that all 4 cards drawn are red.


n(B) = ways in which 4 cards can be selected from 26 red cards.


n(B) = 26C4


P(B) = 26C4/52C4 =


As we need to find the probability of event such that all drawn cards are from same colour. This means we need to find


P(A B)


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


P(E F) = P(E) + P(F) – P(E F)


P(A B) = P(A) + P(B) – P(A B)


As both events A and B have no common elements or we can say that they are mutually exclusive


P(A B) = 0


Hence,


P(A B) = P(A) + P(B) =


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