You have the following coins in your pocket: 5 quarters, 6 dimes, 2 nickels, and 12 pennies. What is the probability you will draw a penny and then a dime?

Answer 1

To find the probability of drawing a penny first and then a dime, we start by determining the total number of coins in your pocket.

1. Count the number of each type of coin:

   • Quarters: 5
   • Dimes: 6
   • Nickels: 2
   • Pennies: 12

2. Calculate the total number of coins: \[ \text{Total coins} = 5 + 6 + 2 + 12 = 25 \]

3. The probability of drawing a penny first: \[ P(\text{Penny}) = \frac{\text{Number of Pennies}}{\text{Total Coins}} = \frac{12}{25} \]

4. After drawing a penny, we do not replace it, so the total number of coins decreases by 1. The new total is: \[ \text{New total coins} = 25 - 1 = 24 \]

5. The number of dimes remains the same at 6. So the probability of then drawing a dime is: \[ P(\text{Dime | Penny}) = \frac{\text{Number of Dimes}}{\text{New Total Coins}} = \frac{6}{24} = \frac{1}{4} \]

6. To find the overall probability of drawing a penny followed by a dime, we multiply the two probabilities together: \[ P(\text{Penny then Dime}) = P(\text{Penny}) \times P(\text{Dime | Penny}) = \frac{12}{25} \times \frac{1}{4} \]

Calculating this: \[ P(\text{Penny then Dime}) = \frac{12 \cdot 1}{25 \cdot 4} = \frac{12}{100} = \frac{3}{25} \]

Thus, the probability of drawing a penny and then a dime is: \[ \boxed{\frac{3}{25}} \]