## Friday, February 19, 2010

### 52 Card Pickup

A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up or face down. The total value of the cards which landed face up is then calculated. (Card values are assigned as follows: Ace=1, 2=2, ... , 10=10, Jack=11, Queen=12, King=13. There are no jokers.)

What is the probability that the total value is divisible by 13?

#### 2 comments:

1. 100%.

ANY number is divisible by 13. The answer just may not be a whole number...

2. I like your answer, Angela. The more complicated (if we assume the answer is a whole number) is very hard to write up. I was hoping someone would come up with something easier! ;-)

There are 2^52 ways for the cards to fall (if we assume each card falls up or down). The hard part is figuring out how many ways the sum adds up to 13. I'm not going into the math here, but the answer is around 7.7%

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