Question

Suppose a game involves flipping a fair coin (so Heads and Tails are equally likely; that is,

one has = =
1
2) with an $ bet. If Heads come up, the payoff for you is $0.5 (that is, you shall earn $0.5 in
addition to your own bet $); if Tails come up, you shall lose the $. Now, you have $1,000 and w

Answer 1

The expected value of the game is -$0.25, meaning you can expect to lose $0.25 on average per game.

Step-by-step explanation:

The subject of this question is Mathematics. The question asks about a game involving flipping a fair coin and the expected outcomes.

To analyze this game, we can calculate the expected value, which is the sum of each possible outcome multiplied by its probability. In this case, if the coin lands on Heads, the payoff is $0.5 and the probability is 0.5. If the coin lands on Tails, the payoff is -$1 and the probability is also 0.5. Therefore, the expected value of this game is (0.5 * $0.5) + (-1 * 0.5) = -$0.25.

This means that on average, for every game played, you can expect to lose $0.25. So, playing this game will not result in long-term profits.