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Math Help - An interesting probability question

  1. #1
    Bar0n janvdl's Avatar
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    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?
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    GAMMA Mathematics
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    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
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by colby2152 View Post
    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.
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    Quote Originally Posted by colby2152 View Post
    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
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    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.
    Last edited by janvdl; January 25th 2008 at 01:13 AM. Reason: Sign error
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    Grand Panjandrum
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    Quote Originally Posted by janvdl View Post
    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
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    GAMMA Mathematics
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    Quote Originally Posted by CaptainBlack View Post
    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

    Now, add them up!
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    Member Henderson's Avatar
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    I'm not entirely sure how I feel about this answer. The math is no problem, and I would agree that .4375 would be correct if we were talking about completely independent events, like the old drawing marbles out of two bags example.

    However, these are not independent in two different senses: The weather on Saturday is undeniably going to influence the weather on Sunday, and the two days flow into each other. Is there one storm front moving through, or is there a fresh one each day? Does the new one come in right at midnight?

    Later on, problems will be more precise and controlled, but at the very beginning of looking into Statistics, it's important to realize that there are outside circumstances and variables infulencing these events.
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by Henderson View Post
    However, these are not independent in two different senses: The weather on Saturday is undeniably going to influence the weather on Sunday...
    You're correct, they are not independent events. How would the solution look then?
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