title: Probability of event
body: <p>Here is a probability problem: you observe .5 cars on average passing in front of you every 5 minutes on a road. What is the probability of seeing at least 1 car in 10 minutes?</p>
  
  <p>I'm trying to solve this in 2 ways. The first way is to say: P(no car in 5 minutes) = 1 - .5 = .5. P(no car in first 5 minutes and no car in second 5 minutes) = P(no car in first 5 minutes) * P(no car in second 5 minutes) by independence. Therefore P(at least 1 car in 10 minutes) = 1 - .5*.5 = .75.</p>
  
  <p>However, if I try the same, with a Poisson distribution with rate lambda = .5 per unit of time, for 2 units of time, I get: P(at least 1 car in 2 units of time) = 1 - exp(-2*lambda) = .63. </p>
  
  <p>Am I doing something wrong? If not, what explains the discrepancy?</p>
  
  <p>Thanks!</p>