If the probability of finding at least one car on the road in 30 minutes is 95%, what is the chance of finding at least one car in 10 minutes?
Let p be the probability of not finding a car in 10 minutes so that the required probability, the probability of finding at least one car in 10 minutes, is 1- p.
The probability of finding no car in 30 minutes is a joint probability of three consecutive intervals of 10 minutes each of no cars. I.e., p x p x p = p3. But this is equivalent to 1 – the probability of finding at least one car in 30 minutes. In other words 1 – p3 = 0.95. p = cube root of (1 – 0.95) = 0.368.
So, the required probability, (1 – p) becomes 1 – 0.368 = 0.63 or 63%
