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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)?
probability of not observing a car in 30 mins = probabality of not observing a car in first 10 mins * not obs in next 10 mins * not obs in last 10 mins
lets assume observing a car in 10 mins = p
probability of not observing the car in 10 mins = 1-p
probability of not observing the car in 30 mins = (1-p)^3
so (1-p)^3 = 0.05
1-p = (0.05)^1/3.
p = 1- (0.05)^1/3.
p = 1- 0.37
p = 0.63.
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