The probability that it will rain this Saturday is 0.56, and the probability that it will rain on Sunday is 0.48. What is the maximum value of the probability that it will rain on neither Saturday nor
Sunday?
I have thought of independence of the 2 events (rain on saturday and rain on sunday), but since the problem does not mention that 2 events are independent, I wonder if there is any solid way to find the probability that it would not rain on both days
Update: I asked my professor and he says independence is not given here
Best Answer
You would want the rain on sat and rain on sun to have as high covariance as possible. Think of the simpler case with 50 percent chance of rain each day. Perfect correlation is then possible -- i.e. it either rains on both days or on none of the days. Then there is a 50 percent chance that there is no rain.
The same logic applies in your case. You want it to rain on both days with 48 percents chance and 8 percents chance it only rains on saturday. Then the prob of rain on none of the days is 44%.