# Wheel Question

• Oct 11th 2009, 08:11 AM
gs.sh11
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 $\displaystyle \frac{a}{b}$ is greater than 1.

The question is attached as an image below.
• Oct 11th 2009, 10:24 AM
Wilmer
(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
• Oct 12th 2009, 08:37 AM
awkward
Quote:

Originally Posted by gs.sh11
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 $\displaystyle \frac{a}{b}$ is greater than 1.

The question is attached as an image below.

$\displaystyle \frac{a}{b} > 1$ if and only if $\displaystyle a > b$.

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.
• Oct 12th 2009, 08:18 PM
HallsofIvy
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.