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 52C2 ways

So total number of element of events = 52C2

 

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 26C2 ways.

There are 4 aces out of which 2 aces can be drawn in 4C2 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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