A popular beach currently has 106 ​visitors, and 56 of them are building sand castles.

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Part 1
What is the probability that a randomly chosen beachgoer is building sand castles​?
Write your answer as a fraction or whole number.
​P(building sand castles​) ​=
  
enter your response here
Write your answer as a decimal rounded to the hundredths place.
​P(building sand castles​) ​=
  
enter your response here
Write your answer as a percent.
​P(building sand castles​) ​=
  
enter your response here​%

1 answer

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!