Tuesday, March 8, 2011

If the probability of observing a car in 30 minutes on a highway is 0.95- Google Asked It

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)?

1st Way

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

2nd Way

You have to look at your probability of NOT seeing a car, which is .05 in 30 minutes. In order to break this down into 10 minute chunks, you need to figure out how you arrived at that probability, which would be x * x * x = .05, so x ^ 3 = .05.

2 comments:

Anonymous said...

Why intervals of 10 min and not 15 min?

Shashank Narayan said...

because question is asked for 10 min. right ?