Probability of rain

I was reading a book about innumeracy and one of the chapters was on probability. This weather woman said 'there is a 50% chance of rain on Saturday, and a 50% chance of rain on Sunday, so the chance of rain this weekend is 100%'

Obviously she was wrong, but it got me thinking how would one calculate the probability of rain that weekend?

I decided to make it simpler by saying P(rain on Saturday) = 0.5 and P(rain on Sunday) = 1.0

This obviously means that P(rain this weekend) = 1.0

I then used trial and error to calculate the chance of rain that weekend

I started with P(rain on Saturday) x P(rain on Sunday) but that gives 0.5

Then I tried P(no rain this weekend) = P(no rain on Saturday) x P(no rain on Sunday) and this gives 0.0

Therefore P(rain this weekend) = 1 - P(no rain this weekend) = 1.0

Using this method, P(rain this weekend) = 0.75 or 75% for the original statement.

Is this the best way to calculate the chance of rain?


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You can calculate it using a tree diagram like so:

I converted the 50% to a fraction. When using probability, any "AND" statements you multiply, so I figured out the chance of it not raining on Saturday AND not raining on Sunday to be 1/4 (or 0.25). Probability always equals to 1, so I took 1/4 away from 1, getting 3/4 (or 0.75)

That's a wrong approach, but the simplicity of the problem gives the right answer nevertheless. A tree diagram implies the chance of rain on a Sunday depends on whether it rains the prev day or not, which is not true by the provided information.

There are only 4 possibilities, and raining on Sunday/Saturday are independent events from one another by the looks of it.

They are:
-Rain on Sat and rain on Sun
-Rain on Sat and no rain on Sun
-No rain on Sat and rain on Sun
-No rain on either day.

What's the probability that it rains on both? That would be rain on Sat x rain on Sun, so $0.5\cdot 0.1=0.05$
What's the probability that is rains on Sat and not on Sun? Well that's $0.5\cdot (1-0.1)=0.45$
What's the probability it doesn't rain on Sat but rain on Sun? That's $(1-0.5)\cdot 0.1=0.05$

Thus the total probability that it will rain on the weekend is 55% by adding up the first 3 possibilities.

The answer for the original one is 75% so you're right. The easiest way to calc it to realise each day has equal chance of raining, so over the two days, each possibility has an each chance of happening. 1/4=0.25 for any possibility, adding up the first 3 gives the answer right away.

I think you used chance of rain on Sunday is 10% not 100%

But I think that's pretty much what I did, isn't it? Not sure.

Ah yeah misread as 0.1. And yes it's pretty much what you've done.

The fastest way is indeed 1-(all unwanted possibilities) and since here it is only a single unwanted possibility, this is the quickest way. Otherwise, just add the first 3 up for it.

just google the weather forecast

no need for all this math