The forecast says a 50% chance of rain on Saturday and a 50% chance on Sunday
The forecast says a 50% chance of rain on Saturday and a 50% chance on Sunday. Tanya says that means it is 100% certain to rain on at least one day of the weekend. Her brother says the real chance is lower than that. Who is right?
Who do you think is right? Pick one.
The answer: Her brother is right, the real chance is 75%, not 100%
Why
Tanya is adding the two chances, which feels natural but double-counts and quickly breaks: by the same logic a 50% chance on each of three days would give 150%, which is impossible. Chances of separate events are not added. The clean way is to ask about the opposite. For it to rain on NEITHER day, Saturday must stay dry (a 50% chance) AND Sunday must stay dry (another 50%), and for both to happen you multiply: 0.5 times 0.5 is 0.25, a 25% chance of a fully dry weekend. So the chance of rain on at least one day is 100% minus 25%, which is 75%. Test: 75% is more than either single day's 50%, since a second chance to rain does help, but it is well short of certain. Her brother is right: the chance is 75% — probabilities of separate events are not added; to combine them you work through what has to happen together.
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