The 'at least one' trick

Goal: Find P(at least one) as 1 − P(none).

Remember: It is usually easier to count the hands with none, then subtract the probability from 1.

1. 1.How many five-card hands contain no ace?

2. 2.What is the probability a five-card hand contains no ace? Give a percentage to 2 decimal places.

3. 3.What is the probability a five-card hand contains at least one ace?

4. 4.Two cards are drawn. What is the probability at least one is a heart?

5. 5.Two cards are drawn. What is the probability at least one is red?

6. 6.Explain in a sentence why counting 'none' is easier than counting 'at least one'.