The GATE Grind

GATE 2021 ME (ME1) – Question 43

Operations Research · Simple queuing models · 2 marks · Multiple choice

Customers arrive at a shop according to the Poisson distribution with a mean of 10 customers/hour. The manager notes that no customer arrives for the first 3 minutes after the shop opens. The probability that a customer arrives within the next 3 minutes is

  1. 0.39
  2. 0.86
  3. 0.50
  4. 0.61

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 0.39

Explanation

Poisson arrivals have independent increments, so the empty first interval does not affect the next one. Its mean count is λt=10(3/60)=0.5.

Probability of one or more is $1-e^{-0.5}=0.393469$, approximately **0.39 (A)**.