Question

martina is at the grand opening celebration of a supermarket. she spins a wheel with 10 equal - sized slices, as shown below. the wheel has 8 black slices, 1 grey slice, and 1 white slice. when the wheel is spun, the arrow stops on a slice at random. if the arrow stops on the border of two slices, the wheel is spun again.
(a) if the arrow stops on a grey slice, then martina wins a gift card. find the odds against martina winning a gift card.
(b) if the arrow stops on a grey slice, then martina wins a gift card. find the odds in favor of martina winning a gift card.

Explanation:

Step1: Calculate the number of non - grey slices

The total number of slices is \(n = 10\). The number of grey slices is \(g=1\). The number of non - grey slices is \(n - g=10 - 1=9\).

Step2: Find the odds against winning

The odds against an event \(E\) (in this case, \(E\) is "winning" which means landing on a grey slice) is given by the ratio of the number of unfavorable outcomes to the number of favorable outcomes. The number of unfavorable outcomes (not landing on grey) is \(9\), and the number of favorable outcomes (landing on grey) is \(1\). So the odds against winning is \(9:1\).

Step3: Find the odds in favor of winning

The odds in favor of an event \(E\) is given by the ratio of the number of favorable outcomes to the number of unfavorable outcomes. The number of favorable outcomes (landing on grey) is \(1\), and the number of unfavorable outcomes (not landing on grey) is \(9\). So the odds in favor of winning is \(1:9\).

Answer:

(a) \(9:1\)
(b) \(1:9\)