Question

latoya won a charity raffle. her prize will be randomly selected from the 9 prizes shown below. the prizes include 4 rings, 4 cameras, and 1 headset.
(a) find the odds in favor of latoya winning a camera.
(b) find the odds against latoya winning a camera.

Explanation:

Step1: Recall the formula for odds in favor

Odds in favor of an event \(E\) is \(\frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}\).
Number of cameras (favorable outcomes) \(n(F)=4\).
Number of non - camera prizes (unfavorable outcomes) \(n(U)=9 - 4=5\).

Step2: Calculate odds in favor

Odds in favor of winning a camera \(=\frac{4}{5}\), which can be written as \(4:5\).

Step3: Recall the formula for odds against

Odds against an event \(E\) is \(\frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}\).
Using \(n(F) = 4\) and \(n(U)=5\).

Step4: Calculate odds against

Odds against winning a camera \(=\frac{5}{4}\), which can be written as \(5:4\).

Answer:

(a) \(4:5\)
(b) \(5:4\)