# Thread: An interesting probability question

1. ## An interesting probability question

Reading through my newly acquired statistics book, I came across the following question:

If a weather forecaster predicts 25% chance of rain for Saturday, and 25% for Sunday as well, does that mean there's a 50% chance of rain over the weekend? Yes or No and explain your answer.

My logic tells me we should take the average, which is 25%, so there should be a 25% chance of rain for the entire weekend. Am i right?

2. Let p be the chance of rain. Raining over the weekend implies that it rains at least one day, so the chances of that happening are $2pq+p^2$. Since $p=.25$ and $q-.75$, then $2pq+p^2 = .375+.0625 \Rightarrow .4375$

3. Originally Posted by colby2152
Let p be the chance of rain. Raining over the weekend implies that it rains at least one day, so the chances of that happening are $2pq+p^2$. Since $p=.25$ and $q-.75$, then $2pq+p^2 = .375+.0625 \Rightarrow .4375$
A bit more complicated than i thought

Thanks Colby.

4. Originally Posted by colby2152
Let p be the chance of rain. Raining over the weekend implies that it rains at least one day, so the chances of that happening are $2pq+p^2$. Since $p=.25$ and $q-.75$, then $2pq+p^2 = .375+.0625 \Rightarrow .4375$
Where does this: $2pq+p^2$ come from?

If raining on Saturday and raining on Sunday are independent then the probability
of it raining on neither is 0.75^2 =0.5625, or the probability of rain on one or more
days is: 1-0.5625=0.4375.

RonL

5. Originally Posted by CaptainBlack
Where does this: $2pq+p^2$ come from?
Well Captain, by using your method and incorporating a variable we can say that the chance of rain is:

$1 - (1 - x)^2 \ \ \ \rightarrow \ \ \ 1 - 1 + 2x - x^2 \ \ \ \rightarrow \ \ \ 2x - x^2$ (Where x = 0,25)

That looks remarkably similar to Colby's formula.

6. Originally Posted by janvdl
Well Captain, by using your method and incorporating a variable we can say that the chance of rain is:

$1 - (1 - x)^2 \ \ \ \rightarrow \ \ \ 1 - 1 + 2x - x^2 \ \ \ \rightarrow \ \ \ 2x - x^2$ (Where x = 0,25)

That looks remarkably similar to Colby's formula.
I don't deny that it is right, it's just that it appears without introduction

RonL

7. Originally Posted by CaptainBlack
I don't deny that it is right, it's just that it appears without introduction

RonL
Yes, no intro was present, but without further a due...

There are three ways it can rain on the weekend:

Rain on Saturday, Not Rain on Sunday: $pq$
Not Rain on Saturday, Rain on Sunday: $qp$
Rain on Saturday, Rain on Sunday: $p^2$