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Math Help - Wheel Question

  1. #1
    Newbie gs.sh11's Avatar
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    Wheel Question

    Hi, Please help me solve this question. I have no idea where to begin, other than knowing that A must be larger than one, because the question asks, 'what is the probability that the fraction \frac{a}{b} is greater than 1.

    The question is attached as an image below.
    Attached Thumbnails Attached Thumbnails Wheel Question-spin.jpg  
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  2. #2
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    (0+1+2+3+4+5) / 36 = 15/36 = 5/9

    0: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6
    ....
    5: 6/1, 6/2, 6/3, 6/4, 6/5, 6/6
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    Quote Originally Posted by gs.sh11 View Post
    Hi, Please help me solve this question. I have no idea where to begin, other than knowing that A must be larger than one, because the question asks, 'what is the probability that the fraction \frac{a}{b} is greater than 1.

    The question is attached as an image below.
    \frac{a}{b} > 1 if and only if a > b.

    From the picture, all values of a from 1 to 6, are equally likely, and the same for b. So all 36 ordered pairs (a,b) are equally likely. List the pairs and count the ones where a > b.
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  4. #4
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    A little more quickly that listing them all: of the 36 pairs, exactly 6 of them are pairs of equal numbers. Of the remaining 30, exactly half, 15 have a> b and the other half have b>a. The probability that, on a single roll, a> b is 15/36= 5/9.
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