I need step by step solution please This Question: 1 pt 4 of 17 (3 complete) dev

Question

I need step by step solution please

This Question: 1 pt 4 of 17 (3 complete) deviatio A card is drawn at random from a standard deck of 52 cards. Find the following conditional probabilities. a) The card is a club, given that it is black 24 b) The card is black, given that it is a club. c) The card is a queen, given that it is black d) The card is a king, given that it is a face card. 3 a) The probability that a card is a club, given that it is black, is (Simplify your answer.) b) The probability that a card is black, given that it is a club, is (Simplify your answer.) ard devi c) The probability that a card is a queen, given that it is black, is (Simplify your answer.) d) The probability that a card is a king, given that it is a face card, is (Simplify your answer.) ndard dev Enter your answer in each of the answer boxes

Explanation / Answer

A) There are 26 black cards and in that, 13 are clubs.

So, P(a card is club | card is black) = 13/26 = 0.5

B) All clubs are black. So, given its club, the probability that its black = 1

C) There are 26 black cards and 2 black queens in it

So, P(queen | black) = 2/26 = 1/13

D) Number of face cards = 4x3 = 12

Number of kings = 4

So, P(king | face card) = 4/12 = 1/3

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