The probability of a car passing a junction in a 20-minute window is 0.9. What is the chance that a car passes the crossroad in a 5-minute window?
Let’s divide the 20-minute duration into four intervals of 5 minutes each. Let p be the probability of a car passing the junction in 5 minutes. Then, the chance of no car in 5 minutes is (1-p). We know the probability of not finding a car for 20 minutes, the joint probability of four such events happening one after another, is 1 – 0.9 = 0.1. Since these four incidents are independent, you can multiply, i.e., it is (1-p)4.
0.1 = (1-p)4
1 – p = (0.1)(1/4)
p = 1 – (0.1)(1/4)= 1 – 0.56 = 0.44
