SOLUTION: A card is drawn from an ordinary deck of cards. What is the probability that the card is a king given that the card is red?

Question 1156973: A card is drawn from an ordinary deck of cards. What is the probability that the card is a king given that the card is red?
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Clearly, 2 red kings out of 26 red cards, so (2/26) =

However, if you want to apply Bayes to solve (just to illustrate):
P(A)*P(B|A) = P(B)*P(A|B)

and
P(A) = probability of king drawn = 4/52 = 1/13
P(B) = probability of a red card drawn = 26/52 = 1/2
P(B|A) = probability of a red card given it is a king = 1/2 (2 red kings / 4 kings total)

P(A|B) = P(A)*P(B|A) / P(B) = (1/2)(1/13) / (1/2) = 1/13, as above

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