Suppose you select a card at random from a standard deck, and then without putting it...

Suppose you select a card at random from a standard deck, and then without putting it back, you select a second card at random from the remaining 51 cards. What is the probability that both cards have the same rank, or both have the same suit, or one is red and one is black?

Expert Solution

The "first" card doesn't matter, as only the second card has to have the same rank. After removing one card, there are 51 cards left in the deck. 3 of them have the same rank as the card that was removed. Hence, the probability of getting dealt a pair is 3/51 = 1/17.

The first card has a chance of 1 of being in some suit, and the second should be 12/51 to be of the same suit, so the total is 12/51

these three probabilities are joined by or statement so we have to add these three probabilities.

3/51+12/51+13/51

=28/51

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orchestra answered 1 year ago

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