Question

Each day Donna and Mary toss a coin to see who buys the other person coffee ​($2.34 a​ cup). One tosses and the other calls the outcome. If the person who calls the outcome is​ correct, the other buys the​ coffee; otherwise the caller pays. Assume that an honest coin is​ used, that Mary tosses the​ coin, and that Donna calls the outcome. Find​ Mary's expected payback. Is this a fair​ game?

Answer 1

Mary's expected payback is $0, making this a fair game.

Step-by-step explanation:

To find Mary's expected payback, we need to calculate the probability of Donna calling the outcome correctly. Since an honest coin is used, the probability of getting heads or tails is 0.5 for each toss. Let's assume Mary tosses the coin and Donna calls it correctly, which happens with a probability of 0.5. In this case, Mary's payback is -$2.34 (the cost of coffee).

Now, let's assume Mary tosses the coin and Donna calls it incorrectly, which also happens with a probability of 0.5. In this case, Mary's payback is $2.34 (the cost of coffee).

To calculate Mary's expected payback, we multiply the payback for each outcome by its probability and sum them up:
Expected payback = (0.5 × -$2.34) + (0.5 × $2.34) = -$1.17 + $1.17 = $0

Mary's expected payback is $0. Since the expected payback is zero, this game is considered fair.

Answer 2

yes

Step-by-step explanation:

Each day Donna and Mary toss a coin to see who buys the other person coffee ​($2.34 a​ cup). One tosses and the other calls the outcome. If the person who calls the outcome is​ correct, the other buys the​ coffee; otherwise the caller pays. Assume that an honest coin is​ used, that Mary tosses the​ coin, and that Donna calls the outcome.