Seemingly simple probability question that stumped me!?

Question

If there is a 50% chance that it will rain on Saturday and there is a 50% chance that it will rain on Sunday. Is there a 100% chance that it will rain on the weekend?! Obviously that doesn't seem right, but since we are talking about an 'or' probability the calculation is 0.5+0.5 = 1.

The problem is that this means there is a 100% chance that it will rain on the weekend as well as a 100% chance that it won't!

I'm missing something obvious I'm sure but what?!

Answer 1

Your probability calculation is wrong.

Think of it like this, on each day it can either rain or not. The two are mutually exclusive. Thus, for the weekend, it can either rain on both days, rain on saturday, rain on sunday, or not rain at all. Rain occurs in 3/4 outcomes, each of which is equally as likely, thus, you have a 75% chance of rain.

You can see this also by considering each as an "and" situation and multiplying the probabilities.

P(Rain Sat, and Sun) = .5*.5 = .25
P(Rain Sat, not Sun) = .5*(1-.5) = .25
P(not Sat: Rain Sun) = (1-.5)*.5 = .25
P(no rain Sat & Sun) = (1-.5)*(1-.5) = .25

Now, you can add the probabilities, and again, adding the probabilities of rain occurance leads to a 75% chance of rain!

Answer 2

the problem is you are trying to use a formula when you should jus tthink about it in its most basic form. If there is a 50/50 chance on each day then it you would have four possible outcomes. The first being that it will rain Saturday and not Sunday. The second is it could rain Sunday but not Saturday. The third is it could rain both days and the fourth is that it could rain neither day. So out of the four possible combinations there are three possible situations which will result in rain so the odds are 3 out of 4 or 75%. Any time you are dealing with 50/50s it can be helpful to thing of it in terms of flipping a coin.

Answer 3

These probabilities only mean for that day say they said a 70% Saturday and 60% Sunday then does that mean 130% chance on the weekend? no. There's only 2 50-50 chances it will rain "this weekend", you can't add them and say its a 100% percent chance because then it is guaranteed it will rain when you and I know there's only a 50% chance each day where it might not rain. Therefore, the obvious thing you were missing was that you don't add the two and stop, you ad the two and divide like an average so if you think about what I just said, say its a 100% chance sat. and a 100% chance on Sunday, you add them to get 200 and divide by 2 to get 100% chance of rain this weekend (you can't have 200%). So in your case the 50% and 50% will add to 100, divided by 2 gives you a 50% chance of rain this weekend hope this helps

Answer 4

It is astounding how few answers to your question are correct! Why do people who clearly have no understanding of probability try to answer? There is a 50% chance that it won't rain on Saturday, and a 50% chance that it won't rain on Sunday. So the chances of it not raining on either day are 0.5 x 0.5 = 0.25. Therefore there is a 75% chance of rain at some point over the weekend.

Answer 5

This is basically thesame as flipping a coin twice in a row. The fallacy here is that Nature has no 'memory' (we like to say that the trials are 'independent') so there are a total of 4 possible outcomes. It rains Saturday, it rains Sunday, it rains both days, or it rains neither day. This means that there is a 25% chance that it won't rain and a 75% chance that it will.


Doug

Answer 6

There's only a 50% chance that it will rain EACH DAY, so instead of adding Saturday and Sunday's chances you'd surmise that there's a 50% chance of rain on the weekend because there's no change in the probability.

Answer 7

There's a 50% chance of rain for the weekend and there's a 50% chance it won't. You don't add the two percentages together. You find the averages. 50 + 50 = 100 / 2 = 50%. So say there is a 30 percent chance of rain on Saturday and 40 percent chance on Sunday. The chance of it raining over the weekend is 35% because 30 + 40 = 70 / 2 = 35%. Understand?

Answer 8

If you are asking what is the probability that it will rain on one of the days then the answer is 75%. Since the probability that it will rain on both days is 0.5*0.5 = 0.25 = 25%, and the probability that it will not rain on any of the days is also 25%. So the remaining 50% is composed of 'it will rain on Saturday but not on Sunday' and 'it will rain on Sunday but not on Saturday'. By adding 25 and 50, you get 75%.

Answer 9

Weather usually depends on previous events.

These events are called 'dependent' events.

For instance, If it rains Saturday (with 50% chance), it will rain Sunday with 90% chance.

If it doesn't rain Saturday (again with 50% chance), it will rain Sunday with 50% chance (as any other day is).

P(rains Sunday) = (.5)(.9) + (.5)(.5) = .45 + .25 = .70 = 70%

This is only one way of looking at it, a lot of factors go into the weather.

Answer 10

75% - doc2be, doug, tlets and a_liberal... have the right approach.

Here's how it works.

Let's say the probability of event A (rain on saturday) is Pa.
The probability of event B (rain on Sunday ) is Pb
And we have to assume that the two events are independent, that is, that rain on Saturday won't change the probability of rain on Sunday.

Then the probability of rain on Both days is Pa * Pb, here 25%.

But you asked about the probability of rain on _either_ day - that will happen _unless_ there is no rain on both days, so its probability is (100% - the probability of no rain. )

Probability of no rain during the weekend is calculated thus:
Probability of no rain Saturday = (1-Pa) = 50%
Probability of no rain Sunday = (1-Pb) = 50%
Probability of no rain on the weekend (1-Pa)*(1-Pb) = 25%

So the probability of some rain is 100% - 25% or 75%.

Bring your umbrella! :)