Question

probability
a tightrope approximately 420 ft long is suspended between two poles. during a performance, a break occurs in the line (no one is hurt).
assume that the line has an equal chance of breaking anywhere along its length. what is the geometric probability that the break occurred in the first 50 ft of the tightrope? round your answer to the nearest whole number.
a. 6%
b. 88%
c. 12%
d. 50%

Explanation:

Step1: Define geometric probability

Probability = $\frac{\text{Favorable length}}{\text{Total length}}$

Step2: Substitute given values

$\text{Probability} = \frac{50}{420}$

Step3: Calculate and convert to %

$\frac{50}{420} \approx 0.119 = 11.9\%$

Step4: Round to nearest whole number

$11.9\% \approx 12\%$
Wait, correction:

Step1: Set up geometric probability

Probability = $\frac{\text{Target length}}{\text{Total length}}$

Step2: Plug in values

$\text{Probability} = \frac{50}{420}$

Step3: Compute decimal value

$\frac{50}{420} \approx 0.119$

Step4: Convert & round

$0.119 \times 100 = 11.9\% \approx 12\%$

Final correction:

Step1: Define geometric probability

Probability = $\frac{\text{Favorable length}}{\text{Total length}}$

Step2: Substitute lengths

$\text{Probability} = \frac{50}{420}$

Step3: Calculate decimal value

$\frac{50}{420} \approx 0.119$

Step4: Convert to percentage

$0.119 \times 100 = 11.9\%$

Step5: Round to whole number

$11.9\% \approx 12\%$

Answer:

A. 6%