# Thread: Probability that a sum of 2 numbers is less than 6

1. ## 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...

2. 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...

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

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.

3. Thank you.

4. No problem! Would you be willing to post your results?