Question 990556: We are drawing two cards without replacement from a standard 52 card deck. Find the probability that we draw at least one black card. The probability is
Answer by ayhseddu(1)   (Show Source):
You can put this solution on YOUR website! Instead of calculating the actual probability we will first calculate the complementary probability which is the probability of drawing 0 black cards or only red cards. After we have found this complementary probability we will reduce it from 1 and thus get the required probability.
If we are drawing two cards without replacement, the total number of ways to draw cards = C(52,2)
There are a total of 26 red cards and 26 black cards.
The number of ways to draw only red cards = C(26,2)
P(only red cards are drawn) = C(26,2)/C(52,2)= 25/102
P(at least one black card is drawn)= 1-P(only red cards are drawn)
P(at least one black card is drawn)= 1-25/102 = 77/102 = 0.75
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