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Thread: Probability

  1. #1
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    Probability

    omg i feel stupid for asking this question cause I cant get it, im probs tired or something, but here it is anyways:

    One layer of tinting material on a window cuts out 1/5 of the sun's UV rays.
    1)what fraction would be cut out by using two layers?
    2) How many layers would be required to cut out at least 9/10 of the sun's UV rays?

    Answers:
    1)9/25
    2)11

    SHOWS me workings!! fanks

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    Re: Probability

    1) after 1 layer , we have 1-0.2 =0.8 passing thru
    so 0.8 get to travel to the 2nd layer, where another 0.2 will be cut out

    2) so it works in the same way as compound interest , only difference is that it "depreciates"
    and a similar example would be
    if the interest rate is 5% p a, how many years would a principal of P double if the interest if compounded annually ?

    so P*(1.05) is the money after 1 year, P*(1.05)*(1.05) is the money after another year
    after n years , we have P*1.05^n which should equal 2*P
    so 1.05^n=2
    take log of both sides
    ln (1.05^n)= ln2
    n *ln 1.05= ln2
    n = ln2 / ln 1.05 = 14.2066...=15 for it to double as it only calculates interest annually

    The question you're asking is very similar, but it has inequality in it
    so be carefully with the inequality signs
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    Re: Probability

    also if u haven't learned log , sub number in and see when it satisfies the inequality

    which sucks when the number is large
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    Re: Probability

    Quote Originally Posted by frmldhyd View Post
    omg i feel stupid for asking this question cause I cant get it, im probs tired or something, but here it is anyways:

    One layer of tinting material on a window cuts out 1/5 of the sun's UV rays.
    1)what fraction would be cut out by using two layers?
    2) How many layers would be required to cut out at least 9/10 of the sun's UV rays?

    Answers:
    1)9/25
    2)11

    SHOWS me workings!! fanks
    This is a series type question, not probability.
    Let x be the amount of the sun's rays that hits the material
    First layer takes out x/5 so after the first layer there is only 4x/5 left that is not cut
    When it hits the second layer, only 4x/5 of rays pass through and a fifth of that is removed
    i.e. (4x/5)(1/5) is removed
    Total amount cut = x/5 + 4x/25 = 9x/25 so fraction of rays cut is 9/25

    Note that after each layer we multiply the amount of rays that entered by 4/5 since 1/5 is removed.
    In terms of proportions:
    After 1st layer the fraction of rays left is (4/5)
    After 2nd layer the fraction of rays left is (4/5)2
    After 3rd layer the fraction of rays left is (4/5)3
    ...
    After nth layer the fraction of rays left is (4/5)n

    We want the fraction of rays left after the nth layer to be at least 1/10 (as 9/10 is cut out) so
    (4/5)n > 9/10
    Using logarithms or otherwise this should yield n = 11 as the lowest integer which satisfies this inequality

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    Re: Probability

    Thanks!!

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    Re: Probability

    Quote Originally Posted by Trebla View Post
    This is a series type question, not probability.
    LOL, I felt that something was not right
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    Re: Probability

    Quote Originally Posted by Trebla View Post
    This is a series type question, not probability.
    Let x be the amount of the sun's rays that hits the material
    First layer takes out x/5 so after the first layer there is only 4x/5 left that is not cut
    When it hits the second layer, only 4x/5 of rays pass through and a fifth of that is removed
    i.e. (4x/5)(1/5) is removed
    Total amount cut = x/5 + 4x/25 = 9x/25 so fraction of rays cut is 9/25

    Note that after each layer we multiply the amount of rays that entered by 4/5 since 1/5 is removed.
    In terms of proportions:
    After 1st layer the fraction of rays left is (4/5)
    After 2nd layer the fraction of rays left is (4/5)2
    After 3rd layer the fraction of rays left is (4/5)3
    ...
    After nth layer the fraction of rays left is (4/5)n

    We want the fraction of rays left after the nth layer to be at least 1/10 (as 9/10 is cut out) so
    (4/5)n > 9/10
    Using logarithms or otherwise this should yield n = 11 as the lowest integer which satisfies this inequality
    i believe you have a made a mistake but please correct me if i am wrong
    where you wrote (4/5)^n>9/10, it is meant to be (4/5)^n<1/10 as the number of layers you want to cut out is 9/10 and leave 1/10 light remaining
    thanks
    Roy G Biv likes this.

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