cars on road  solution ???
if the probability of observing a car in 20 minutes on a highway is 609/625, what is the probability of observing a car in 5 minutes (assuming constant default probability)?
Abyss
Wednesday, June 22, 2005
let x be the probability of seeing the car in 5 mins. we assume constant default probabilty so for every 5 mintue interval the distribution is the same
probability of seeing the car in 20 mins =
probability of seeing the car in first 5 mins or
probability of not seeing the car in first 5 minsinterval but in the next 5 mins (10 minute) or
probablity of not seeing the car both in the first and second 5 mins interval and seeing it in the third 5 mins(15 minute)
or
probabilty of not seeing it in first, second and third 5 minute and seeing it in the fourth 5 minute interval(20 mins)
so
x + (1x)x + (1x)(1x)x + (1x)(1x)(1x)x = 609/625
solving the above cubic equation for values x < 609/625
Abyss
Wednesday, June 22, 2005
3/5. You have correct equation, but there is a way to get to the answer without using a pen.
DK
Wednesday, June 22, 2005
yeh i see it.that is by taking the converse right
probability of not seeing the car in 20 mins = (probability of not seeing the car in 5 mins)^ 4
as we can assume constant default probability
probability of not seeing tha car in 5 mins = (1  (609/625))^ (1/4) = 2/5
so probability of seeing the car in 5 mins = 1  (2/5) = 3/5
Abyss
Wednesday, June 22, 2005
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