Final answer:
To find the expected value of drawing a single coin from a student's pocket with different coin types and quantities, one multiplies the value of each coin by its draw probability and sums them. This calculation provides the average value one would get from many draws.
Step-by-step explanation:
Calculating the Expected Value of a Coin Draw
The expected value of drawing a single coin, given the amounts of different coins the student has, is calculated by multiplying the value of each coin by the probability of drawing that type of coin and then summing these products. First, we need to determine the total number of coins, which is 5 pennies + 4 nickels + 6 dimes + 2 quarters + 1 dollar coin = 18 coins. The probability of drawing each type of coin is the number of that type of coin divided by the total number of coins. The expected value (EV) is:
- Pennies: (5/18) * $0.01
- Nickels: (4/18) * $0.05
- Dimes: (6/18) * $0.10
- Quarters: (2/18) * $0.25
- Dollar coin: (1/18) * $1.00
Now, we add up the expected values:
EV = (5/18) * $0.01 + (4/18) * $0.05 + (6/18) * $0.10 + (2/18) * $0.25 + (1/18) * $1.00
After performing the calculations, we find the expected value of drawing a single coin from the pocket. This value represents the average monetary outcome one would receive if they were to repeat the coin drawing process many times.