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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?

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Answer:

1/5

Step-by-step explanation:

The stick has a length of 5 units

The stick is broken at two points chosen at random

First break: the probability that you get a piece that is 1 unit or longer than 1 units= 1/5.

Second break, the probability that you get a piece that is 1 unit or longer than 1 units is 1/5.

Therefore,

The total probability =probability of first break * probability of second break * original stick unit

=1/5 * 1/5 * 5

= 1/25 *5

=5/25

=1/5