Suppose busses arrive at a bus stop either with an inter-arrival time of exactly 1 min or with an inter-arrival time of exactly 10 mins. Suppose the 1 min inter-arrival times occur with probability 2/3 and the 10 min inter-arrival times occur with probability 1/3. What is the average inter-arrival time between bus arrivals? .What is the probability that a person, arriving uniformly at random, lands in the 10 min inter-arrival time?
Answers to questions are 4 and 5/6 respectively.
For the first one I tried solving it this way: either it is 10 min interval or 1 min interval so multiplied each one with their probabilities, adding them up and then taking reciprocal (as the average in exponential is 1/lambda). But that seems to be wrong. And for secondly I have no clue