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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

Kareem is at a grand opening celebration of a supermarket. He spins the wheel with-example-1

1 Answer

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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}

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