Question

Three cards are selected at random from a group of 7. Two of the cards have been marked with winning numbers. What is the probability that exactly 1 of the 3 cards has a winning number?

Answer 1

There are `7C_3` ways of choosing 3 cards from the deck. That's the total number of outcomes.

If you end up with the 2 unmarked and 1 marked card:

• there are `5C_2` ways of choosing 2 unmarked cards from the 5, and

• `2C_1` ways of choosing 1 marked cards from the 2.

So the probability is:

`(5C_2 cdot 2C_1)/(7C_3) = 4/7`