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O COUNTING AND PROBABILITY

Finding the odds in favor and against

Susana v

Espoo

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 I 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.

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(a) If the arrow stops on a black slice, then Keith wins a gift card. Find the

odds against Keith winning a gift card

to

X

Р

(b) 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.

Explanation

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Respuesta :

MrRoyal

Answer:

a. [tex]Odds = \frac{3}{7}[/tex]

b. [tex]Odds = \frac{7}{3}[/tex]

Step-by-step explanation:

Given

[tex]n(Black) = 7[/tex]

[tex]n(Grey) = 2[/tex]

[tex]n(White) = 1[/tex]

[tex]n(Total) = 10[/tex]

Solving (a): Odds against winning

Since, the arrow must stop at black, then

The odds against winning is calculated as thus:

[tex]Odds = \frac{n(Total) - n(Black)}{n(Black)}[/tex]

[tex]Odds = \frac{10 - 7}{7}[/tex]

[tex]Odds = \frac{3}{7}[/tex]

Solving (b): Odds in favor of winning

Since, the arrow must stop at black, then

The odds is calculated as thus:

[tex]Odds = \frac{n(Black)}{n(Total) - n(Black)}[/tex]

[tex]Odds = \frac{7}{10 - 7}[/tex]

[tex]Odds = \frac{7}{3}[/tex]

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