# Puzzle | Probability of a Truck Passing

• Difficulty Level : Hard
• Last Updated : 30 Aug, 2017

The probability of a truck passing a certain intersection in a 20 minute windows is 0.9. What is the probability of a truck passing the intersection in a 5 minute window? (Assuming a constant probability throughout)

Solution
Let p be the probability of a truck passing the intersection in a 5 minute window.

Probability of a truck passing in a 20 minute window = 1 – (probability of no truck passing in a 20 minute window)
Probability of a truck passing in a 20 minute window = 1 – (1 – probability of a truck passing in a 5 minute window)^4

```0.9 = 1 – (1 – p)^4
(1 – p)^4 = 0.1
1 – p = 10^(-0.25)
p = 1 – 10^(-0.25) = 0.4377 ```

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