**Question:**

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

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C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

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**Solution:** This is one of the basic probability questions asked in a software interview. Let’s start by creating an equation. Let **x** be the probability of a car passing the intersection in a 5-minute window.

Probability of a car passing in a 20-minute window = 1 – (probability of no car passing in a 20-minute window)

Probability of a car passing in a 20-minute window = 1 – (1 – probability of a car passing in a 5-minute window)^4

0.9 = 1 – (1 – x)^4

(1 – x)^4 = 0.1

1 – x = 10^(-0.25)

x = 1 – 10^(-0.25) =

Probability of a car passing in a 20-minute window = 1 – (1 – probability of a car passing in a 5-minute window)^4

0.9 = 1 – (1 – x)^4

(1 – x)^4 = 0.1

1 – x = 10^(-0.25)

x = 1 – 10^(-0.25) =

**0.4377**That was simple eh. Ready for a challenge? Have a look at some of the other probability questions.