You are given a stack of 15 subway Metro Cards:

8 have no funds left, 3 have $2.00 each, and 4 have $3.00 each

You hear the train coming. If it takes more than 3 swipes to get in, you will miss the train.

What is the probability of that happening if you keep randomly selecting Metro Cards from the stack to swipe until you find one that works?

Assume that if a card doesn't work, (i.e. not enough founds, you throw it away rather than return it to the stack).

A subway ride costs $2.75