Passengers repeatedly try to reserve a seat in any train between two stations until successful. If a passenger has a 40% chance of getting a reservation in any attempt, the average number of attempts needed to reserve a seat is ________.
Treat attempts as independent trials with constant success probability p=0.4. The count N includes the successful attempt and follows a geometric distribution on 1,2,3,….
Its mean is $E[N]=1/p=1/0.4=$ **2.5 attempts**. Counting only unsuccessful attempts would instead give $(1-p)/p=1.5$, which is not what is asked.
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