Chapter 13, Problem 8MCQ

a.

To determine

To calculate:

Probability that break will occur in the first $50m$ of the tightrope.

Answer to Problem 8MCQ

Probability that break will occur in the first $50m$ of the tightrope is $16\%$ .

Explanation of Solution

Given information:

Length of tightrope: $320m$ .

Calculations:

It is given that line has equal chance of breaking anywhere along its length.

The first $50m$ form $\frac{50}{320}\times 100\approx 16\%$ of the total length.

Therefore, the probability that a break will occur in the first $50m$ of the tightrope is about $16\%$ .

b.

To determine

To calculate:

Probability that break will occur within $20m$ of a pole.

Answer to Problem 8MCQ

Probability that break will occur within $20m$ of a pole is $13\%$ .

Explanation of Solution

Given information:

Length of tightrope: $320m$ .

Calculations:

The line has an equal chance of breaking anywhere along its length.

The first and last $20m$ form $\frac{20+20}{320}\times 10\approx 13\%$ of the total length.

Thus, probability that a break will occur within $20m$ of a pole is about $13\%$ .