Final answer:
The expected value of a game of chance is determined by multiplying each outcome's value by its probability and summing the products. A positive expected value suggests potential profit over time, while a negative value indicates a likely loss. Specific details of each game's payouts and odds are needed to compute the expected value.
Step-by-step explanation:
The calculation of the expected value in a game of chance involves multiplying the value of each possible outcome by its probability and then summing these products. To find the expected winnings from the scenarios provided, we would need more specific information about the payouts and odds of the game being played. The question appears to be asking for the expected value of several different games involving drawing cards from a deck, tossing a coin, or playing a slot machine. Without the specific details about the payouts for each outcome, it is not possible to calculate the expected value.
In general, the formula for expected value when playing a game is:
Expected Value (EV) = Sum of (Probability of Outcome x Value of Outcome)
To determine whether you should play a game based on the financial outcomes, you must calculate the EV. If the EV is positive, you can expect to come out ahead over the long run. If it is negative, you can expect to lose money over time.