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# What is the probability that two cards randomly selected from a standard 52 card deck are a black card followed by a Jack if the first card

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What is the probability that two cards randomly selected from a standard 52 card deck are is a red card followed by a King if the first card is not replaced after it is drawn?

May 6, 2021

#1
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Split this into 2 scenarios, first, the probability of drawing a red king then a red card. Then, the probability of drawing a black king then a red card. Finally, add them together. :))

=^._.^=

May 6, 2021
#2
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I think you have the porblem backwards? We draw the red card first, so that may affect the probabilty of drawing a king after. How do I acount for this?

BWStar  May 6, 2021
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Ohh, I do have it backwards.

First, the probability of drawing a red card is 26/52 = 1/2.

2/52 of them are red kings.

24/52 of them are red cards.

If we start by drawing a red king, there are 3 kings left, 3/51. So the chance we draw a red king, then another king is 2/52*3/51.

If we start by dawing a red card that if not a king, there are 4 kings left, 4/51. So the chance we draw a red card (non king), then a king is 24/42*4/51.

Adding the chances together, 24/42*4/51 + 2/52*3/51. :))

Please tell me if there are any mistakes or questions.

=^._.^=

catmg  May 6, 2021