Question

keith is at the grand opening celebration of a supermarket. he spins a wheel with 10 equal - sized slices, as shown below. the wheel has 7 black slices, 2 grey slices, 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 black slice, then keith wins a gift card. find the odds in favor of keith winning a gift card. (b) if the arrow stops on a black slice, then keith wins a gift card. find the odds against keith winning a gift card.

Explanation:

Step1: Define favorable and non - favorable outcomes

The number of black slices (favorable outcomes for winning) is $n_{f}=7$, and the number of non - black slices (grey + white) is $n_{nf}=2 + 1=3$.

Step2: Calculate odds in favor

The odds in favor of an event is the ratio of the number of favorable outcomes to the number of non - favorable outcomes. So, the odds in favor of Keith winning a gift card is $\frac{n_{f}}{n_{nf}}=\frac{7}{3}$, or $7:3$.

Step3: Calculate odds against

The odds against an event is the ratio of the number of non - favorable outcomes to the number of favorable outcomes. So, the odds against Keith winning a gift card is $\frac{n_{nf}}{n_{f}}=\frac{3}{7}$, or $3:7$.

Answer:

(a) $7:3$
(b) $3:7$