Answer to Question #337584 in Statistics and Probability for Moey

Question

A

child plays with a pair of scissors and

a piece of string 10 cm long. He cuts the string

into two at a randomly chosen place.

What is the probability that the piece of string to the left

of the pair of scissors is less than 4 cm long?

Answer 1

Continuous uniform distribution

Let X be length of string to the left of the pair of scissors. $X ∼ U(0, 10).$

The density function of the continuous uniform random variable X on the

interval $[0, 10]$ is

$$f(x) = \begin{cases} \dfrac{1}{10} &0\le x\le10 \\ 0, &\text{elsewhere } \end{cases}$$

$$P(X<4)=\dfrac{4}{10}=\dfrac{2}{5}=0.4$$