Chapter 11.8, Problem 12WE

(a)

To determine

To Find: The probability that each pieces will be at least $2cm$ long.

Answer to Problem 12WE

  $0.5$

Explanation of Solution

Given: A piece of string $8cm$ is long is cut at a random point.

Probability that one of the pieces will be shorter than $2cm$

  $\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$

Therefore

Probability that both pieces are longer than $2cm$

  $1-\frac{1}{2}=\frac{1}{2}=0.5$

Hence, the probability is $0.5$ .

(b)

To determine

To Find: The probability that length of two pieces differ by no more than $2cm$ long.

Answer to Problem 12WE

  $0.25$

Explanation of Solution

Given: A piece of string $8cm$ is long is cut at a random point.

The place to cut the $8cm$ string to make the pieces differ by more than $2cm$ is by cutting anywhere up to the first $2cm$

Therefore

Probability that length of two pieces differ by no more than $2cm$ long

  $\frac{1}{8}+\frac{1}{8}=\frac{1}{4}=0.25$

Hence, the probability is $0.25$ .

(c)

To determine

To Find: The probability that length of two pieces total $8cm$ .

Answer to Problem 12WE

  $1$

Explanation of Solution

Given: A piece of string $8cm$ is long is cut at a random point.

Probability that length of two pieces total $8cm$ .

  $\frac{8}{8}=1$

Hence, the probability is $1$ .