In this question, even the times at which the shuttle arrives are being counted. Like if we start from 12, then we are also considering that if the person arrives at 12:20 which is also the time at which the local shuttle arrives as a part of the outcomes in which the person will have to wait for more than 6 minutes. But they arrive at the same time so why are we considering that the person will wait till 12:35 when the local shuttle too arrives at 12:20?
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"Even the times at which the shuttle arrives are being counted"
The solution writes "Between 20:00 and 29:00" -- the 20 here is simply the label for where that gap starts (a shuttle just left at minute 20). It is NOT saying minute 20 itself is a bad outcome. The actual bad arrivals are the ones just after minute 20, i.e. 20:01, 20:02, all the way up to 20:29.
"The person arrives at 12:20, which is also when the local shuttle arrives, and is counted as a wait > 6 outcome"
It is not. A person arriving at exactly 12:20 boards immediately, waits 0 minutes, and is not a "wait > 6" case. The solution is not claiming otherwise.
"Why are we considering that the person will wait till 12:35 when the local shuttle arrives at 12:20?"
We are not considering that. The interval "20 to 29" means passengers who arrive at 12:21, 12:22, ..., 12:28 -- people who just MISSED the 12:20 shuttle and now must wait for the 12:35 one. None of them are the person who arrives at 12:20.
So why does the solution write "20 to 29" if 20 is not included?
Because in a continuous probability model, the single point t = 20 has zero length and contributes zero probability. Writing [20, 29) or (20, 29) or "20 to 29" all give the same length of 9 minutes. The boundary point is irrelevant to the final answer.
Academic discussion and doubt solving for: Logarithms, Set Theory, Matrices & Determinants, Permutation & Combination, Probability, Binomial Theorem
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Then bhaiya, 12:21 to 12:28 shouldn't be counted as 8 outcomes only as a person who arrives at 12:29 would wait exactly 6 minutes and not longer than 6 minutes.