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Math Help - Probability Question

  1. #1
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    Probability Question

    Hello everyone,

    Thank you in advance for any help that you may be able to offer me!

    The following problem is really close to the actual problem on my homework, and I am trying to figure out which probability formula/approach I should use for the following statistics problem?

    Let's say that there are 14 voters and they are randomly selected from a population of 150,000 voters (40% of whom are Republicans), and all 14 were Republicans.

    How do I find the probability of getting 14 Republicans when 14 voters are randomly selected from this population?

    My solution:

    .4^14 = 2.68

    Is this right?
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  2. #2
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    F.Y.I when addressing problem regarding probability take note that probability cannot be smaller than zero or greater than 1. Therefore your answer 2.68 is not correct.

    You have to use the (Discrete) Binomial random variable to address the problem mentioned.

    Formula : P( X = x ) = ( n C x )(p)^x(1-p)^n-x
    substitute these figures into the formula above and you will be able to derive the answer
    n =150,000, x = 14,p=0.4

    Quote Originally Posted by BFG12 View Post
    Hello everyone,

    Thank you in advance for any help that you may be able to offer me!

    The following problem is really close to the actual problem on my homework, and I am trying to figure out which probability formula/approach I should use for the following statistics problem?

    Let's say that there are 14 voters and they are randomly selected from a population of 150,000 voters (40% of whom are Republicans), and all 14 were Republicans.

    How do I find the probability of getting 14 Republicans when 14 voters are randomly selected from this population?

    My solution:

    .4^14 = 2.68

    Is this right?
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  3. #3
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    Still need help here!

    tester85,

    Thank you for your help; however, I tried using this formula for the problem I have to solve and I ran into two problems:

    A) This problem is in a chapter of my book where binomial probabilities haven't been introduced yet.

    B) When applying n = 150,00 to (nCx), I can't even get a result because I think that 150,000! throws an overload on my calculator.

    Any help would be appreciated!
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  4. #4
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    Quote Originally Posted by BFG12 View Post
    Hello everyone,

    Thank you in advance for any help that you may be able to offer me!

    The following problem is really close to the actual problem on my homework, and I am trying to figure out which probability formula/approach I should use for the following statistics problem?

    Let's say that there are 14 voters and they are randomly selected from a population of 150,000 voters (40% of whom are Republicans), and all 14 were Republicans.

    How do I find the probability of getting 14 Republicans when 14 voters are randomly selected from this population?

    My solution:

    .4^14 = 2.68

    Is this right?
    BFG12,

    You have the right formula but your arithmetic is faulty.

    0.4^{14} = 2.68 \cdot 10^{-6},

    approximately. Technically this formula gives an exact result only if you sample with replacement, but with your large population there is almost no difference between sampling with and without replacement.

    (tester85, you have the wrong idea-- your formula would require taking a sample of 150,000 from the population (with replacement) and finding exactly 14 republicans.)
    Last edited by awkward; December 16th 2008 at 04:40 PM. Reason: can't type
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  5. #5
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    Sorry guys i misunderstood the problem. Thanks awkward for pointing it out.
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  6. #6
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    got it........

    40% of 150000 is 60000

    probablity of getting a republican= 60000/150000=18/45

    probablity of getting two republican=18/45 multiplied with (18-1)/(45-1)

    similarly proceed until you have subtracted 14 times

    mutiply all and simplify and you wil get the answer
    Last edited by mr fantastic; December 27th 2008 at 03:17 AM. Reason: Deleted all the smilies.
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  7. #7
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    Quote Originally Posted by susrut View Post
    40% of 150000 is 60000

    probablity of getting a republican= 60000/150000=18/45

    probablity of getting two republican=18/45 multiplied with (18-1)/(45-1)

    similarly proceed until you have subtracted 14 times

    mutiply all and simplify and you wil get the answer
    This is not correct. The probability of gettting the second Republican is obviously NOT 17/44. It's (60000 - 1)/( 150000 - 1) = 59999/149999.

    Similarly for the second, third etc. Republican. The probability of the fourteenth Republican is obviously NOT (18 - 13)/(45 - 13) = 5/32. It's (60000 - 13)/( 150000 - 13) = 59987/149987.

    The correct answer has been given and discussed by awkward.

    And please don't abuse the smilies.
    Last edited by mr fantastic; December 27th 2008 at 03:19 AM.
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