Averages and expected value

Goal: Compute expected values and use linearity: E[count] = n × (target cards ÷ 52).

Remember: Expected value is the long-run average. It need not be a value a single trial can produce.

1. 1.Five cards are drawn. What is the expected number of hearts?

2. 2.Thirteen cards are drawn. What is the expected number of aces?

3. 3.Classroom scoring exercise: a number card scores 0 points, a face card 1 point and an ace 3 points (the points are only a counting device). What is the expected score of one card?

4. 4.Four cards are drawn. What is the expected number of face cards?

5. 5.Seven cards are drawn. What is the expected number of red cards?

6. 6.A fair six-sided die is rolled. What is the expected value?

7. 7.True or false: the expected value must be a number that can actually occur on a single trial. Give an example.