# 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?

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?

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

#### Explanation:

First card non-winning: $\frac{5}{7}$

Second card non-winning: $\frac{4}{6} = \frac{2}{3}$

Third card non-winning: $\frac{3}{5}$

$P \left(\text{non-winning}\right) = \frac{\cancel{5}}{7} \times \frac{2}{\cancel{3}} \times \frac{\cancel{3}}{\cancel{5}} = \frac{2}{7}$

$P \left(\text{at least one winning}\right) = 1 - \frac{2}{7} = \frac{5}{7}$

##### Add Answer of: 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?
Similar Homework Help Questions

• ### If each lottery has only one winning ticket, and you buy one ticket to each of the two lotteries, what is the probability that you will have at least one winning ticket

If each lottery has only one winning ticket, and you buy one ticket to each of the two lotteries, what is the probability that you will have at least one winning ticket? INFORMATION THAT MIGHT BE IMPORTANT IN ORDER TO SOLVE THIS QUESTION There are two little lotteries in town, each of which sells exactly 100 tickets.

• ### what is the probability of winning a lottery game where the winning number is made of 6digits from 0-9 chosen at random

what is the probability of winning a lottery game where the winning number is made of 6digits from 0-9 chosen at random?i do not undestand how to solve please help

• ### Three consecutive even numbers have a sum of 84. What is the least number?

Need Online Homework Help?