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Three cards are randomly drawn from a standard deck of $52$ cards, without replacement. Find the probability that the first card is a king, the second card is hearts, and the third card is red.

 Jan 30, 2024
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The probablility for the first card to be a king is 1/13

the probability for the second card to be hearts is 3/4 likely to be 1/4 or and 1/4 likely to be 3/13

The probablity for the third to be red is 3/4 likely 1/2 or 1/4 likely 6/13

 

(1/13*3/4*1/4 +1/13*1/4*3/13) *3/4*1/2+

(1/13*3/4*1/4 +1/13*1/4*3/13) *1/4*6/13

=

2601/281216​

 Jan 30, 2024

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