Shuffle a standard deck of cards and cut it into

Montenovofe

Montenovofe

Answered question

2022-07-02

Shuffle a standard deck of cards and cut it into three piles. What is the probability that a face card will turn up on top of one of the piles?
There are 12 face cards (four jacks, four queens and four kings) in the deck.

Answer & Explanation

soosenhc

soosenhc

Beginner2022-07-03Added 16 answers

As has been mentioned in the comments, the split into three decks is just a red herring - the problem is equivalent to just picking the three top cards assuming the deck has been shuffled well.
The probability of getting at least one court card is equal to one minus the probability of the inverse case: getting no court cards at all.
The probability of getting no court cards is fairly easy to compute. First, we have 40 non-court cards to choose from a deck of 52, then 39 non-court cards from a deck of 51 and finally 38 non-court cards from a deck of 50. This makes the probability of getting no court cards in three picks
40 52 × 39 51 × 38 50 = 59280 132600
This means probability of getting at least one court card is 1 59280 132600 = 73320 132600 which is approximately 0.55

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