2 cards are drawn at random from a pack of 52 cards. find the probability that the cards are either both red or both aces.

Out of 52 cards, two cards can be drawn in ^{52}C_{2} ways

So total number of element of events = ^{52}C_{2}

Consider the following event.

A = Two cards drawn are red cards

B = Two cards drawn are aces.

Required probability = P (A ∪ B)

= P (A) + P (B) – P (A ∩ B)

Now there are 26 red cards at of which 2 red cards can be drawn in ^{26}C_{2 }ways.

There are 4 aces out of which 2 aces can be drawn in ^{4}C_{2 }ways.

and there are two cards which are both red and aces

Hence Required probability = P(A) + P(B) – P(A ∩ B)

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