To find the probability that a randomly chosen beachgoer is building sand castles, we can use the formula for probability:
\[ P(\text{building sand castles}) = \frac{\text{number of visitors building sand castles}}{\text{total number of visitors}} \]
Given that there are 56 visitors building sand castles and a total of 106 visitors, we can calculate the probability as follows:
Part 1: Fraction
\[ P(\text{building sand castles}) = \frac{56}{106} \]
We can simplify this fraction by finding the greatest common divisor (GCD) of 56 and 106, which is 2:
\[ P(\text{building sand castles}) = \frac{56 \div 2}{106 \div 2} = \frac{28}{53} \]
So, the fraction is: \[ \text{P(building sand castles)} = \frac{28}{53} \]
Part 2: Decimal
To convert the fraction \(\frac{28}{53}\) into a decimal, we perform the division:
\[ P(\text{building sand castles}) \approx 0.52830188 \]
Now, rounding this to the hundredths place:
\[ P(\text{building sand castles}) \approx 0.53 \]
Part 3: Percent
To convert the decimal into a percentage, we multiply by 100:
\[ P(\text{building sand castles}) \approx 0.53 \times 100 = 53.00% \]
Summary of Answers:
- As a fraction: \( P(\text{building sand castles}) = \frac{28}{53} \)
- As a decimal: \( P(\text{building sand castles}) = 0.53 \)
- As a percent: \( P(\text{building sand castles}) = 53.00% \)
Feel free to ask if you have more questions!