Final answer:
The expected value of drawing a single coin from the student's pocket is approximately $0.29, which is calculated using the values of the coins and their probabilities of being drawn.
Step-by-step explanation:
To calculate the expected value of drawing a single coin, we need to know the value of each coin type and the probability of drawing each type. The student has a total of 18 coins:
- 5 pennies (each worth $0.01)
- 4 nickels (each worth $0.05)
- 6 dimes (each worth $0.10)
- 2 quarters (each worth $0.25)
- 1 dollar coin (worth $1.00)
- The expected value (EV) is calculated using the formula:
- EV = (Σ value of coin * probability of drawing that coin)
The probabilities for each are:
- Penny: 5/18
- Nickel: 4/18
- Dime: 6/18
- Quarter: 2/18
- Dollar: 1/18
Now, we calculate the EV:
- (0.01 * 5/18) + (0.05 * 4/18) + (0.10 * 6/18) + (0.25 * 2/18) + (1.00 * 1/18)
EV = $0.2861 (rounded to the nearest cent)
So, the expected value of drawing a single coin out of the student's pocket is approximately $0.29.