The probability that it will rain today is 0.5.The probability that it will rain tomorrow is 0.6.The probability that it will rain either today or tomorrow is 0.7.What is the probability that it will rain today and tomorrow?
Why we just can't multiply the probability of today's and tomorrows' raining, as they are two events and must be followed one after other to get the final event on raining on two days. So the answer is 0.3.
But the solution say we got to use the equality Pr(A and B) = Pr(A) + Pr(B) - Pr(A or B). This give us the answer 0.4.
It look to me like Independence is to do something in here, but I might be wrong.
Please help me with, why set notation works but not the product rule ?