7.11 Expected Value
The long-run average payoff of a repeated experiment, found by weighting outcomes by their probabilities, and used to judge whether a bet is fair.
2 exercises
7.11 Exercise 3
Interpret the expected values of the following experiments.
- Roll a standard 6-sided die and note the number showing.
- Roll 2 standard 6-sided dice and note the sum of the numbers showing.
- Draw a card from a well-shuffled standard deck of cards and note its Rummy value (15 for aces; 10 for tens, jacks, queens, and kings; 5 for everything else).
7.11 Exercise 5
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.
- At one casin…
Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.