To find the probability of randomly selecting a quarter from the jar, we can use the following formula:
\[ P(\text{quarter}) = \frac{\text{number of quarters}}{\text{total number of coins}} \]
First, let's calculate the total number of coins in the jar:
- Number of nickels = 70
- Number of dimes = 100
- Number of quarters = 80
- Number of 1 dollar coins = 50
Total number of coins:
\[ 70 + 100 + 80 + 50 = 300 \]
Now, we can use the number of quarters and the total number of coins to find the probability:
\[ P(\text{quarter}) = \frac{80}{300} \]
To express the probability as a percentage, we multiply by 100:
\[ P(\text{quarter}) = \frac{80}{300} \times 100 \]
Calculating that gives:
\[ P(\text{quarter}) = \frac{80 \times 100}{300} = \frac{8000}{300} \approx 26.67% \]
Therefore, the probability of selecting a quarter from the jar is approximately 26.67%.