Question

Find the expected value (or expectation) of the games described. A bag contains two silver dollars and eight slugs. You pay 50 cents to reach into the bag and take a coin, which you get to keep.

Answer 1

The expected value of the game is found by multiplying each possible outcome by its probability of occurring and summing up the results. In this case, the expected value of the game is -$0.20.

Step-by-step explanation:

The expected value of a game is found by multiplying each possible outcome by its probability of occurring and then summing up the results. In this case, there are 10 total coins in the bag, 2 of which are silver dollars and 8 of which are slugs. The probability of selecting a silver dollar is 2/10 or 0.2, and the probability of selecting a slug is 8/10 or 0.8.

The possible outcomes and associated amounts are as follows:

• If you select a silver dollar, you would get to keep it, so the amount is $1.
• If you select a slug, you would lose the 50 cents you paid to play the game, so the amount is -$0.50.

To find the expected value, multiply each outcome by its probability and sum up the results:

E(X) = (0.2 * $1) + (0.8 * -$0.50)

E(X) = $0.20 + (-$0.40)

E(X) = -$0.20

So, the expected value of the game is -$0.20, which means that on average, you would expect to lose 20 cents per game.