There are 3 black and 7 white balls in the box, identical in touch. You draw 3 balls randomly. If you find 1 black ball among the drawn ones, you will win $1, if you find 2 black balls, you win $2 and you will win $10, if all 3 are black. What are the chances to win at least 1 buck?

Question

zehanz · Answer

This sounds complicated, until you realize it is 1 - P(you win nothing).
You win nothing if there are no black balls among the drawn ones.
So calculate 1-P(3 white).