Final answer:
The question deals with Mathematics, specifically probability and expected value. In the provided scenario, you calculate the expected outcome of repetitive plays, given the probabilities of different outcomes and their corresponding payouts. The example shows a calculation leading to an expected loss, demonstrating the concept of expected value in a simple game.
Step-by-step explanation:
The question's subject is Mathematics, and it pertains to probability and expected value calculations, which are often taught in Middle School or High School math courses.
The key concept here is assessing the long-term expected outcome of a game based on the chances of various possible results occurring and their associated payouts.
Example Calculation:
For a biased coin, if the probability of getting heads (P(heads)) is 3/4 and tails (P(tails)) is 1/4, and the payouts are -$6 for heads and $10 for tails, the expected value (EV) can be calculated as:
- EV = (P(heads) * payout for heads) + (P(tails) * payout for tails)
- EV = (3/4 * -6) + (1/4 * 10)
- EV = -4.5 + 2.5
- EV = -2
Thus, if you play this game many times, the expected outcome is a loss of $2 per game on average.