Question

Kareem is at a grand opening celebration of a supermarket. He spins the wheel with 10 equal-size slices, as shown below. The wheel has 7 black slices, 2 grey slices, and 1slice. When the wheel is spun the arrow stops on a random slice. If the arrow stops on the boarder of 2 slices the wheel spins again

Answer 1

Step 1. The wheel has 10 slices:

7 slices are black

2 slices are grey

1 slice is white

Required: Find the odds against and the odds in favor of Kareem winning a gift card if he wins it if the arrow stops on a black slice.

Step 2. The odds are defined as follows:

`\begin{gathered} Odds\text{ against }=\frac{Number\text{ of unfavorable outcomes}}{Number\text{ of favorable outcomes}} \\ Odds\text{ in favor}=\frac{Number\text{ of favorable outcomes}}{Number\text{ of unfavorable outcomes}} \end{gathered}`

Step 3. Solving part (a)

Remember that he wins it if the arrow stops on a black slice, therefore, the number of unfavorable outcomes are all of the slices that are not black which are 3:

`Number\text{ of unfavorable outcomes: 3}`

And the number of favorable outcomes is the number of black slices:

`Number\text{ of favorable outcomes: 7}`

the odds against are:

`\begin{gathered} Odds\text{ aga}\imaginaryI\text{nst}=\frac{Number\text{ of unfavorable outcomes}}{Number\text{ of favorable outcomes}} \\ \downarrow \\ Odds\text{ aga}\imaginaryI\text{nst}=(3)/(7) \end{gathered}`

Step 4. Using the same information, we calculate the odds in favor to solve part (b):

`\begin{gathered} Odds\text{ }\imaginaryI\text{n favor}=\frac{Number\text{ of favorable outcomes}}{Number\text{ of unfavorable outcomes}} \\ \downarrow \\ Odds\text{ }\imaginaryI\text{n favor}=(7)/(3) \end{gathered}`

Answer:

`\begin{gathered} (a)\text{ }(3)/(7) \\ (b)\text{ }(7)/(3) \end{gathered}`