# Category Archives: Multiplication rule

## A strange deck of cards

In a non-standard deck of cards there are

• 20 blue cards (numbered 1 through 20),
• 20 green cards (numbered 1 through 20), and

20 red cards (numbered 1 through 20)

Four cards are dealt without replacement from this deck.

1. What is the probability that exactly two of the four cards dealt are blue?
2. Given that at least one of the first two cards dealt is blue, what is the probability that exactly three of the four cards dealt are blue?
3. What is the probability that at least two of the four cards dealt have the same numeric value (1 through 20)?

## Repeated Quiz Questions

Each week you get multiple attempts to take a two-question quiz. For each attempt, two questions are pulled at random from a bank of 100 questions. For a single attempt, the two questions are distinct.

1. If you attempt the quiz 5 times, what is the probability that within those 5 attempts, you’ve seen at least one question two or more times?
2. How many times do you need to attempt the quiz to have a greater than 50% chance of seeing at least one question two or more times?