An ordinary deck of 52 playing cards is randomly divided into 4 piles of 13 cards each. Let F be the event that the aces of spades and diamonds are in di↵erent piles, and E be the event that the aces of hearts, spades and diamonds are in di↵erent piles. (There are a total of 4 aces in the deck, ace of diamonds, ace of hearts, ace of spades and ace of clubs.) The conditional probability P (E|F) is:

Question

Mathematics

Messiah Fernandez

2 February, 00:03

An ordinary deck of 52 playing cards is randomly divided into 4 piles of 13 cards each. Let F be the event that the aces of spades and diamonds are in di↵erent piles, and E be the event that the aces of hearts, spades and diamonds are in di↵erent piles. (There are a total of 4 aces in the deck, ace of diamonds, ace of hearts, ace of spades and ace of clubs.) The conditional probability P (E|F) is:

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Jaime Ross · Answer 1

0.52

Step-by-step explanation:

In order to calculate P (E|F), we can make the piles by assigning a different number for each card from 1 to 52. The first pile is represented by the first 13 numbers, the second one is represented from the 14th one to the 26th one and so on. If we assume that the ace of spades and diamonds are on different piles, then for the ace of hearths to be on another pile we have only 26 numbers available (the 26 numbers of the remaining two piles) from a total of 50 (the 50 remaining numbers not selected yet). This means that

P (E|F) = 26/50 = 0.52

I hope that works for you!