Hi,
Thanks for posting the problem.
I think this can be clarified with a contingency table for the fate of all timetabled trains:
actually actually
runs cancelled
reported A B
running
reported C D
cancelled
If A, B, C, D are expressed as percentages then clearly A + B + C + D = 100.
"90% of trains actually run" => A + C = 90
so 10% are actually cancelled => B + D = 10
"90% of reports are correct" => A + D = 90
Plugging all this in, the contingency table must take the form
actually actually
runs cancelled
reported A A-80
running
reported 90-A 90-A
cancelled
By my reckoning, "A" (the percentage of timetabled trains that are reported running and do actually run) cannot be explicitly determined from the given information, although it must lie somewhere between 80% and 90% since all probabilities must be greater than or equal to 0.
I agree with the conclusion that half of the trains which are reported cancelled do actually run. ( (90-A)% of all timetabled trains are reported cancelled but actually run. Equally (90-A)% of all timetabled trains are reported cancelled and are in fact cancelled.)
I know - I should get out more