Sure, let's solve this step by step:
We are given the following information about the coins in a piggy bank:
- 5 quarters
- 7 dimes
- 12 nickels
First, let's find the total number of coins.
[tex]\[ \text{Total number of coins} = 5 (\text{quarters}) + 7 (\text{dimes}) + 12 (\text{nickels}) = 24 \][/tex]
### a) P(quarter)
The probability of drawing a quarter can be found by dividing the number of quarters by the total number of coins.
[tex]\[ P(\text{quarter}) = \frac{\text{Number of quarters}}{\text{Total number of coins}} = \frac{5}{24} \approx 0.2083 \][/tex]
### b) P(dime)
Similarly, the probability of drawing a dime is the number of dimes divided by the total number of coins.
[tex]\[ P(\text{dime}) = \frac{\text{Number of dimes}}{\text{Total number of coins}} = \frac{7}{24} \approx 0.2917 \][/tex]
### c) P(nickel)
The probability of drawing a nickel is the number of nickels divided by the total number of coins.
[tex]\[ P(\text{nickel}) = \frac{\text{Number of nickels}}{\text{Total number of coins}} = \frac{12}{24} = 0.5 \][/tex]
So to summarize, the probabilities are:
a) [tex]\( P(\text{quarter}) \approx 0.2083 \)[/tex]
b) [tex]\( P(\text{dime}) \approx 0.2917 \)[/tex]
c) [tex]\( P(\text{nickel}) = 0.5 \)[/tex]
