A box contains 4 coins: a penny, a nickel, a dime, and a quarter. It costs a dime to reach in and take a coin. What is the expected value of this game?
(1/4)(1 + 5 + 10 + 25) cents
That is 10.25 cents.
If you bet a dime, it is still a good bet. You would have a 2.5% edge over the "house"
no guys !!!!!!
To find the expected value of a game, we need to calculate the probability of each possible outcome and multiply it by the corresponding value.
In this game, the possible outcomes are selecting each of the four coins from the box. Since it costs a dime to play, the value of each outcome is the value of the coin minus 10 cents.
Let's calculate the probabilities and values for each outcome:
1. Penny: Probability = 1/4, Value = $0.01 - $0.10 = -$0.09
2. Nickel: Probability = 1/4, Value = $0.05 - $0.10 = -$0.05
3. Dime: Probability = 1/4, Value = $0.10 - $0.10 = $0.00
4. Quarter: Probability = 1/4, Value = $0.25 - $0.10 = $0.15
Now, let's calculate the expected value:
(Expected value) = (Probability of outcome 1 * Value of outcome 1) + (Probability of outcome 2 * Value of outcome 2) + (Probability of outcome 3 * Value of outcome 3) + (Probability of outcome 4 * Value of outcome 4)
= (1/4 * -$0.09) + (1/4 * -$0.05) + (1/4 * $0.00) + (1/4 * $0.15)
= -$0.0225 - $0.0125 + $0.00 + $0.0375
= $0.0025
Therefore, the expected value of this game is $0.0025.