Suppose the probability of rain on day 1 is $p_1$ and probability of rain on day 2 is $p_2$. Then the probability of rain for the entire two-day period is $1-(1-p_1)(1-p_2)$, under the assumption that the two days are independent.
Now my question is: if the independence assumption does not hold true, the probabilities cannot be simply multiplied together and the probability of rain for the two-day period could potentially take on different values depending on the level of dependence between the two days. In this case, what would be a range for the probability of rain during the two-day period?
I really do not have much of a clue to this one. Any help is much appreciated. Thanks!