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Suppose you draw two cards from a deck of 52 cards without replacement.
1) What is the probability that both cards are hearts?
2) What is the probability that exactly one of the cards is hearts?
3) What is the probability that none of the cards are hearts?
I get that the first answer is 13/52 * 12/51.
For the second, is it 13/52 * 39/51 because the new deck has 51 cards of which 12 are hearts, hence 39/51 is the probability of the second not being hearts?
Will the third answer just be 39/52 * 38/51?
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Humaira C.
1 Expert Answer
Raymond B. answered • 09/05/22
Math, microeconomics or criminal justice
1st card is Ace, 2nd is black (spade or club), out of 52 standard deck of cards
4 Aces out of 52 = 4/52 = 1/13 chance of an Ace on one random draw
without replacement 2nd card is black, which was originally 1/2 the deck 26 out of 52 cards
but since one card was removed and not replaced, what's left is still the same odds, since we don't know what color the ace was. Without replacement or with replacement would have made no difference in this problem.
(1/13) x (1/2) = 1/26 = probability of Ace, then Black card
P(A then B) = 1/26 = about 0.0385 = about 3.85%