Take a deck of cards labeled 1-60. Shuffle well and flip over the first 10 cards in a row from left to right.

Let x represent the number of cards in a row from the left that are in ascending order.

For example if the cards were 3 15 22 59 40 7 19 30 33 34 then x=4. The streak ends with the 59 because 40 is less.

Find a formula for p(x), the probability the first x cards are in ascending order and card x+1 is lower than card x, where x={1,...,10}

Generalize: For a deck of c cards labeled 1 to c and flipping over a row of n cards. Find a formula for p(x) where x={1,...,n}

(In reply to Solution by Joel)

Nice work, Joel.

Recursively, p(x) = p(x-1)*x/((x+1)*(x-1))

This made it easy to calculate on a spreadsheet.

I haven't worked out why this probabilities sum to 1, but clearly they do.

Posted by Steve Herman on 2006-10-11 08:15:03