Wednesday, September 29, 2010

Probability Card Trick From Scam School

Just for fun, from Scam School. A simple probability trick. Given 1 deck of 52 cards. There are
a) 12 face cards ( 4 suits of J, Q, K)
a) 40 non-face cards ( 4 suits of 1, 2, ... 9)

Shuffling and separating the deck into 3 pile of cards, what are the odds of getting any face card at the top of the 3 piles? Without thinking, most people believed the chances are lower than chances of all face cards since there are so few face cards. However, the calculation shows otherwise:

Chnaces of getting at least 1 face card in 3 piles
= 1 - Chances of getting all face card
= 1 - (40/52 * 39/51 * 38/50)
= 0.552941176

Therefore, it is slightly more likely to get at least 1 face card due to probability.

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