Question 116155: If two cards are drawn without replacement from a deck, find the probability that the second card is red, given the first card was a heart?
Found 2 solutions by checkley71, Fombitz:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! THE FIRST CARD BEING A HEART REDUCES TO NUMBER OF RED CARDS BY 1. THUS THERE IS ONLY 25 RED CARDS LEFT.
SO WE HAVE 25 RED CARDS OUT OF 51 TOTAL CARDS:
25/51=.49 OR 49% OF THE TIME THE SECOND CARD WILL BE A RED CARD.
Answer by Fombitz(32388)  (Show Source):
You can put this solution on YOUR website! 52 cards
26 are red, 26 are black
13 hearts, 13 diamonds, 13 clubs, 13 spades
First card was a heart, P(heart) = 13/52
Without replacement, the total number of cards is now 51.
51 cards
25 are red, 26 are black
12 hearts, 13 diamonds, 13 clubs, 13 spades
Second card was red (w/o replacement, first card heart), P(red)=25/51
The probabilities then multiply
P(heart and red, wo replacement) = 13/52*25/51= 325/2652 = 0.12
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