Question

A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?

Answer 1

4/25 = 0.16

Explanation:

The shortest stick must be between 0 and 5/3. The probability that it is longer than 1 is therefore:

(5/3 − 1) / (5/3 − 0)

(2/3) / (5/3)

2/5

So the probability that both of the shortest sticks are longer than 1 is (2/5)² = 4/25.