Probability

Question 1

7.11 Example 7.37: Find the expected values of the following experiments.
1. Roll a standard 6-sided die and note the number showing.

Answer 1

3.5 (p.808)

Question 2

7.11 Example 7.37: Find the expected values of the following experiments.
2. Roll two standard 6-sided dice and note the sum of the numbers showing

Answer 2

7 (p.808)

Question 3

7.11 Example 7.39: In the casino game keno, a machine chooses at random 20 numbers between 1 and 80 (inclusive) without replacement.
Players try to predict which numbers will be chosen. Players don’t try to guess all 20, though; generally, they’ll try to
predict between 1 and 10 of the chosen numbers. The amount won depends on the number of guesses they made and
the number of guesses that were correct.
1. At one casino, a player can try to guess just 1 number. If that number is among the 20 selected, the player wins $2;
otherwise, the player loses $1. What is the expected value?

Answer 3

-$0.25 (p.814)

Question 4

7.11 Example 7.39: In the casino game keno, a machine chooses at random 20 numbers between 1 and 80 (inclusive) without replacement.
Players try to predict which numbers will be chosen. Players don’t try to guess all 20, though; generally, they’ll try to
predict between 1 and 10 of the chosen numbers. The amount won depends on the number of guesses they made and
the number of guesses that were correct.
2. At the same casino, if a player makes 2 guesses and they’re both correct, the player wins $14; otherwise, the player
loses $1. What is the expected value?

Answer 4

-$0.10 (p.814)

Question 5

7.11 Example 7.39: In the casino game keno, a machine chooses at random 20 numbers between 1 and 80 (inclusive) without replacement.
Players try to predict which numbers will be chosen. Players don’t try to guess all 20, though; generally, they’ll try to
predict between 1 and 10 of the chosen numbers. The amount won depends on the number of guesses they made and
the number of guesses that were correct.
3. Players can also make 3 guesses. If 2 of the 3 guesses are correct, the player wins $1. If all 3 guesses are correct, the
player wins $42. Otherwise, the player loses $1. What is the expected value?

Answer 5

-$0.13 (p.814)