The probability of rainfall in City X on any given day is 30%. The probability of rainfall on any given day is independent of whether it rains on any other day.
Quantity A: The probability of rainfall in City X on at least one day out of two days.
Quantity B: The probability of no rainfall in City X on either of those two days.
The solution suggests Quantity A is .3+.3-.09=.51, while Quantity B is .7*.7=.49.
My question with quantity A is why are we removing the probability that it rains both days (.09)? If it rains both days, it still rains at least 1 day. Raining both days is raining at least 1 day. If quantity A has said the "probability of rain on one day" as opposed to "at least one day" then this is clearly p(a)+p(b)-p(ab), where I am going off track?
Help!
Jake