Answer
$19
Work Step by Step
The law of large numbers shows that as the sample size increases, the experimental probability tends closer to the theoretical probability.
This means that if we calculate the expected value using the theoretical probabilities of the events occurring, this will be very close to the average payoff per game.
We are told that the probability of winning 10 dollars is 0.9 and that the probability of winning 100 dollars is 0.1.
To find the expected value of this game, we multiply the 'payout' of each event by its probability and add these products together:
$10 \times 0.9 + 100 \times 0.1 = 19$
The average payout per game is 19 dollars.
