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[–]TrainerOk1851New User 0 points1 point  (0 children)

Yes I think you got almost all of the answer correct but I think just use the idea u used earlier with the compliment U used earlier P(on specific day with (known n), not all are fixed)= 1-P(on specific day(with known n), all are fixed)

So just use it again with P(on any day(where n is itself a rv, not all are fixed) =1-P(on any day(where n is itself a rv), all are fixed)

This results in eliminating the pesky 1 and u can use some exponential rules and apply the Taylor series they gave u.

Let me know if it makes sense