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Discrete Mathematics
Probability & Combinatorics
GATE 2013
Medium

Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

  • A8/(2e³)
  • B9/(2e³)
  • 17/(2e³)
  • D26/(2e³)

Explanation

P(X=k) = e^(−3)·3^k/k!. P(fewer than 3) = P(0)+P(1)+P(2) = e^(−3)(1 + 3 + 4.5) = 8.5·e^(−3) = 17/(2e³).

Source: GATE CS 2013 (2013)

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