Thread: Probability of observing car

If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?

Let p is a probability to see a car in 10 minutes.
Then (1-p) is probability NOT to see a car in 10 minutes.
Then probability NOT to see a car in 30 minutes is (1-p)*(1-p)*(1-p).
(1-p)^3 == 0.05
So p = 1-0.05^(1/3)~ 0.63

suppose man reaction time is x
probability to see a car in reaction time is : p
(p)^n=0.95
p= (0.95)^1/n

total reaction time in 30min is nx
nx=1800

P= (0.95)^x/1800


probability is see car in 10min is
(0.95)^x/1800 * 600
= (0.95)^x/3