SOLUTION: There are 26 red cards and 26 black cards in a standard deck of playing cards, for a total of 52 cards. There are 4 kings to a deck, two of which are red kings and two of which are

Algebra ->  Probability-and-statistics -> SOLUTION: There are 26 red cards and 26 black cards in a standard deck of playing cards, for a total of 52 cards. There are 4 kings to a deck, two of which are red kings and two of which are      Log On


   

Question 1186526: There are 26 red cards and 26 black cards in a standard deck of playing cards, for a total of 52 cards. There are 4 kings to a deck, two of which are red kings and two of which are black kings. A card will be randomly selected from a standard deck of playing cards. Let A represent selecting a king and let B represent selecting a red card. Calculate the following probabilities:
P (A) =

P (A ׀ B) =

Based on these probabilities, are A and B independent events? Explain your reasoning.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
P(A) = P(king) = 4/52 = red%281%2F13%29

P(A|B) = P(king|red) = P(king & red)/P(red) = %282%2F52%29%2F%2826%2F52%29+=+2%2F26+=+red%281%2F13%29.
So P(A) = P(A|B). It is also easy to see that P(B) = 26%2F52++=+%282%2F52%29%2F%284%2F52%29+=+1%2F2 = P(B|A). Therefore, A and B are independent events.

Alternatively, P(A & B) = 2%2F52+=+%284%2F52%29%2A%2826%2F52%29 = P(A)*P(B), and so again A and B are independent events.