It is time to end the madness! Here is a logical way to think about the math weather problem that has stumped everyone for the past 3 days. Let me start by restating the problem.
According to the National Weather Service there is a 90% chance of rain today, an 80% chance of rain on Thursday, and a 50% chance of rain on Friday. What is the probability that it will rain on all 3 days?
Consider day one where the probability of rain is 90%. Imagine, for the sake of simplicity, that there are 100 homes within the forecast area. The prediction implies that 90 of them would receive rain and 10 of them would not…as indicated by the aqua blue shading in the following graphic.
So, going into day 2, there is an 80% chance of rain for each of the 100 homes. That means that 80% of the 90 homes that received rain on day one will receive rain today, as will 80% of the homes that did not receive rain on day one. That implies that 72 homes would have received rain on both days. At this point it does not matter if the 10 homes that received no rain on day one get rain today because it is impossible for those homes to have rain every day. In the graphic below the “orange” shading shows the number of homes with rain both days. The “aqua” shows the homes that received rain on just day one. “Yellow” indicates the homes that just got rain on day two, and the “white” shading indicates that we can expect 2 homes, or just 2%, to have not gotten any rain.
On the third day we need only consider the 72 homes that have seem rain on the first two days. Since the probability of rain on the third day is 50% then half of the 72 homes are expected to receive rain on the third day as well. That means 36 of the 100 homes can expect to receive rain everyday for three days.
In simple math terms: .90 x .80 x .50 = .36
Yes, it is a multiplication problem! So, let’s try again.
The National Weather Service indicates the probability of rain for the next three days as 60% today, 40% tomorrow, and 40% on Monday. What is the chance of seeing rain on all three days?
Well, class….it is .60 x .40 x .40. The chance is 9.6%…not very likely!
Kudos to you if you put up with all of that. I don’t blame you if you didn’t. Just remember….multiply, multiply, multiply, multiply! Do not take an average!