A two-day conference is going to be held in a city. The leading newspaper in the city says there is a 10% chance of rain on the first day of the conference and a 40% chance of rain on the second day.
If the newspaper’s figures are correct, the chance that it rains in the city during the conference is:

at least 0%, but we can’t get a better lower bound with the information given.
at least 10% but it might be less than 40%.
at least 40%.

Question

A two-day conference is going to be held in a city. The leading newspaper in the city says there is a 10% chance of rain on the first day of the conference and a 40% chance of rain on the second day.
If the newspaper’s figures are correct, the chance that it rains in the city during the conference is:


at least 0%, but we can’t get a better lower bound with the information given.
at least 10% but it might be less than 40%.
at least 40%.

anonymous · Answer

i would say at least 40% since it is 40% for one day alone

anonymous · Answer

Let A be the event that it rains on the 1st day, B be the event that it rains on the 2nd day. Since the question doesn't mention anything about the independence of the two events, nor we can deduce it, we can only use the fact that P(A and B) <= P(A) and P(A and B) <= P(B). Of course P(A and B) >= 0. So the 0<=P(A and B)<=10%