SOLUTION: Two cards are drawn in succession from a standard 52 card deck. What is the probability that both cards are red If the cards are drawn without replacement IF the cards are dra

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Question 844937: Two cards are drawn in succession from a standard 52 card deck. What is the probability that both cards are red
If the cards are drawn without replacement
IF the cards are drawn with replacement
Found 2 solutions by Fombitz, mark_henrhiz:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
With replacement,
P%28R%2CR%29=%281%2F4%29%281%2F4%29=1%2F16
Without replacement,
P%28R%2CR%29=%2813%2F52%29%2812%2F51%29=%281%2F4%29%284%2F17%29=1%2F17

Answer by mark_henrhiz(40) About Me  (Show Source):
You can put this solution on YOUR website!
In a standard deck of cards there are

13 RED DIAMOND CARDS
13 RED HEART CARDS
13 BLACK CLUB CARDS
13 BLACK SPADE CARDS

A) WITHOUT REPLACEMENT
P(A) = probability that the first card is red
P(B|A) = probability that the second card is red given the first card is also red

P(both are red cards) = P(A)P(B|A)
P(both are red cards) = 26/52 * 25/51
P(both are red cards) = 25/102 = 0.245

B) WITH REPLACEMENT
P(both are red cards) = P(A)P(A|B)
P(both are red cards) = 26/52 * 26/52
P(both are red cards) = 1/4 = 0.25