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Math Help - probability on a set of numbers

  1. #1
    Ka9
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    probability on a set of numbers

    Two numbers a and b, are randomly selected without replacement from the set {2,3,4,5,6}. What is the probability that the fraction a/b is less than 1 and can be expressed as a decimal? Express answer in a fraction.

    My approach to this problem is:
    totally there are 5 numbers and once a number is taken from the set, it is not put back. So with one selection(1/5), two numbers have gone and so, for the second 1/3 and what about the remaing one number. I am afraid my approach is totally wrong.

    Please guide me.

    Thanks,
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  2. #2
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    Quote Originally Posted by Ka9 View Post
    Two numbers a and b, are randomly selected without replacement from the set {2,3,4,5,6}. What is the probability that the fraction a/b is less than 1 and can be expressed as a decimal? Express answer in a fraction.

    My approach to this problem is:
    totally there are 5 numbers and once a number is taken from the set, it is not put back. So with one selection(1/5), two numbers have gone and so, for the second 1/3 and what about the remaing one number. I am afraid my approach is totally wrong.

    Please guide me.

    Thanks,
    \frac{a}{b}<1

    \frac{2}{3},\;\frac{2}{4},\;\frac{2}{5},\;\frac{2}  {6},\;\frac{3}{4},\;\frac{3}{5},\;\frac{3}{6},\;\f  rac{4}{5},\;\frac{4}{6},\;\frac{5}{6}

    are all less than 1.

    In fact, you only need to select 2 f the 5 numbers to be able to form such a fraction.

    Some of these cannot be expressed as a decimal..
    For example...

    \frac{2}{3}=0.6............ with the 6 repeating indefinately.

    How many more cannot be expressed as decimals?
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  3. #3
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    they have given 5 numbers {2,3,4,5,6}

    you take any pair (a,b) (that is select any 2 numbers)

    if a/b>1 then b/a<1 (ex: if 6/4 >1 then 4/6 <1)

    therefore no. of fraction less than 1 will be equal to no. of fraction more than 1, formed using the given numbers.

    probability=1/2
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  4. #4
    Ka9
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    2/3,2/6,4/6,5/6 are repeating indefinately.
    Among 10 possible fractions, only 4 are repeating indefinately. So, naturally the perfect one's are 6 out of 10. So, the answer is 6/10 i.e 3/5

    Correct me.
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  5. #5
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    Yes,
    if we can (which I have done) interpret the question as asking
    "what is the probability of forming a non-repeating decimal which is <1".
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  6. #6
    Ka9
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    Thanks for guiding me. Thanks a lot.
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