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 at least one of the 3 cards has a winning number?

Answer 1

Let's first look at the probability of no winning card:

Explanation:

First card non-winning: `5/7`

Second card non-winning: `4/6=2/3`

Third card non-winning: `3/5`

`P("non-winning")=cancel5/7xx2/cancel3xxcancel3/cancel5=2/7`

`P("at least one winning")=1-2/7=5/7`