Rainy Day

The probability of it raining on Saturday is 60%, on Sunday 30%. What's the range of probability that it doesn't rain over the weekend?


Solution:

Doesn't rain on Saturday: 40%. Let this be event A.
Doesn't rain on Sunday: 70%. Let this be event B.

If the two events are independent: 28%.
Else: P(A & B) = P(A intersect B).
min P(A intersect B): clearly 10%.
max P(A intersect B): clearly 40%.

So the range is 10% to 40%.