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It is not difficult to solve the 16 problem with the great god of mathematics (this year's Beijing college entrance examination math liberal arts problem).
Solution: From (1) 1 to 13, the air quality index is less than 100 in 6 of these 13 days, so the probability is 6/ 13.
(2) There are 13 cases for staying for 2 days, among which four cases (namely, 4, 5, 5, 6, 7, 8, 8, 9) are involved in heavy pollution for only one day, so the probability is 4/ 13.
(3) From the 6th, the variance is the largest on 6th, 7th and 8th.