Question

raina won a charity raffle. her prize will be randomly selected from the 9 prizes shown below. the prizes include 7 rings, 1 camera, and 1 headset. (a) find the odds against raina winning a headset. (b) find the odds in favor of raina winning a headset.

Explanation:

Step1: Calculate number of non - headset prizes

There are 9 prizes in total and 1 headset. So the number of non - headset prizes is $9 - 1=8$.

Step2: Find odds against winning a headset

The odds against an event is the ratio of the number of unfavorable outcomes to the number of favorable outcomes. For not winning a headset (unfavorable outcome of winning a headset), the odds against winning a headset is $8:1$.

Step3: Find odds in favor of winning a headset

The odds in favor of an event is the ratio of the number of favorable outcomes to the number of unfavorable outcomes. For winning a headset, the number of favorable outcomes is 1 and the number of unfavorable outcomes is 8. So the odds in favor of winning a headset is $1:8$.

Answer:

(a) $8:1$
(b) $1:8$