If the probability of observing a car in X minutes on a highway is P, what is the probability of observing a car in X/N minutes (assuming constant default probability)?

X,P,N - can take form of specific numbers like

X=30 minutes
P=0.80
N=10 minutes


Company where asked this question: Google, Microsoft
1 Answer 
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Written by CMaster


Ok, as there is no takers, I will provide my own answer. The key here is to understand that if P is probability of seeing car in X minutes, then (1-P) is a probability of not seeing car in the same amount of time. So, keeping this in mind we can draw following conclusions:

(1-P) is a Probability of not seening car in X minutes once or combined probability of not seeing car in N intervals of X/N, so as the probability multiplies then we can say that probability of not seeing a can in X/N interval will be P1 such as P1^N=(1-P)

And the proability of seeing can in X/N interval will be 1-P1, so resolving the equations we will get:

P1=Log_n(1-P)/N

The answer is 1-Log_n(1-P)/N


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