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Math Help - Probability that a sum of 2 numbers is less than 6

  1. #1
    No one in Particular VonNemo19's Avatar
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    Probability that a sum of 2 numbers is less than 6

    Hi.

    Here it is:

    What is the probability that given two different spinners with the numbers 0-7 on one and the numbers 0-9 on the other, that the sum of the result of spinning both is less than six or the value of the first spinner is less than 3.

    I don't know where to start, but I've graphed the inequality x+y<6, and I think that the number of possibilities for the sum is 18?

    I don't know what to do...
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  2. #2
    Super Member TheChaz's Avatar
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    I would identify the sample space. While you don't necessarily need to list every element, you should at least get the "gist" of it...

    \begin{matrix}<br />
00 &01  &02  &03  &04  &05  &06  &07  &08  &09 \\ <br />
 10&  11&12  &13  &14  &15  &16  &  &  & \\ <br />
 20&21  &22  &23  &24  &  &  &  &  & \\ <br />
 30& 31 &32  &33  &34  &35  &36  &37  &38  &39 \\ <br />
 40&  41& 42 &  &  &  &  &  &  & \\ <br />
 50&  51&  &  &  &  &  &  &  & \\ <br />
 60&  &  &  &  &  &  &  &  & \\ <br />
 70&  &  &  &  &  &  &  &  etc& <br />
\end{matrix}

    Here, the first digit is the spin of the (0-7); the second digit is the spin of the (0-9).

    It was too tiresome to list them all, but I HAVE included everything we need to do this problem.

    1. How many elements are in the sample space?
    2. How many elements are in the event (sum < 6 or First = 3)?
    Hint: Don't count the element "32" twice!

    3. Divide your result from 2 by the result from 1. This is your probability.
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Thank you.
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  4. #4
    Super Member TheChaz's Avatar
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    No problem! Would you be willing to post your results?
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