I approached this problem two ways:


The simple way, giving each trial a 51/52 chance of failure with 52 trials giving (51/52)^52 =36.43% which means I'm under the 40% chance required to take your bet.


I then needed to confirm to myself that each trial was independent becuase it felt wrong, so i assumed the first deck came through in order As.2s.3s etc

Obviously the chances of first card matching is 1/52.

The 2s will have a 1/51 chance of SUCCESS every time it wasn't the first card which is 51/52 of the time so we get 1.51/51.52 or 1/52.

The 3s will have a 1/50 chance of SUCCESS every time it's not one of the first two cards (50/52) so again we get 1.50/50/52 or 1/52.


So these trials can be treated as independent i believe.


My maths is rusty so please check this for yourselves and flame me if approppriate.


Lori