Question

The nine regions on a spinner are numbered with positive integers 1 through 9, and the probability of the spinner landing on a given region is proportional to the label for that region. For example, since $4 \times 2 = 8$, the probability of landing on 8 is twice the probability of landing on 4. What is the probability that this spinner will land on an odd number? Express your answer as a common fraction.

Answer 1

odd sum ... 1 + 3 + 5 + 7 + 9 = 25

even sum ... 2 + 4 + 6 + 8 = 20

p(odd) = 25 / (25 + 20)

Answer 2

let the area of the whole spinner be x
fraction of areas:
1 ---- 1/x
2 ---- 2/x
...
9 ---- 9/x
total area = 45/x
area of odds = 1/x + 3/x + 5/x + 7/x + 9/x = 25/x

prob(odd) = (25/x) / (45/x) = 25/45 = 5/9