Q: What is the average number of cards you need to draw from a well shuffled deck of cards before you get an Ace?

The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)

A:There is a lot of discussion on the web on using hypergeometric distributions for solving these kind of problems. The hypergeometric distribution is just a big word for something fairly simple. Here is the wikipedia explanation for it (link).

But an easier "smarter" way to solve this puzzle (along with ones that fit this framework) is to work with expectations and indicator random variables. Indicator random variables are like on/off switches. They are 1 under certain conditions, 0 otherwise.

Let us assume that the deck of cards (52 total) is as follows, it has 4 aces and all others are labelled X. Let \(Z_i\) represent the indicator variable for a card in position \(i\) with value set as 1 when all aces are in behind it, 0 otherwise.

The total number of draws will then be

$$ N = \sum_{i=1…

The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)

A:There is a lot of discussion on the web on using hypergeometric distributions for solving these kind of problems. The hypergeometric distribution is just a big word for something fairly simple. Here is the wikipedia explanation for it (link).

But an easier "smarter" way to solve this puzzle (along with ones that fit this framework) is to work with expectations and indicator random variables. Indicator random variables are like on/off switches. They are 1 under certain conditions, 0 otherwise.

Let us assume that the deck of cards (52 total) is as follows, it has 4 aces and all others are labelled X. Let \(Z_i\) represent the indicator variable for a card in position \(i\) with value set as 1 when all aces are in behind it, 0 otherwise.

The total number of draws will then be

$$ N = \sum_{i=1…