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two cards are drawn from a pack of 52 cards. What is the probability that either both are aces or both are black?

two cards are drawn from a pack of 52 cards. What is the probability that either both are aces or both are black?

Grade:Upto college level

1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
Two cards are drawn from a pack of 52 cards.
A deck contains 26 black cards out of which 2 are drawn.
Hence P (2 black) = 26C2 / 52C2
A deck contains 4 acess out of which 2 are drawn.
Hence, P (2 black) = 4C2 / 52C2
P ( either both black or both ace) = 26C2 / 52C2 + 4C2 / 52C2 - 2C2 / 52C2
= (26C2 + 4C2 - 2C2) / 52C2
= (650 + 10)/ 2652
= 330/ 1326.
This is the required answer.
Thanks & Regards
Latika Leekha
askIITians Faculty

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