Question

Abbi, Bella and Claire are playing a game with a spinner. The spinner has 5 equal-sized sections: one yellow (Y), one red (R), one blue (B), one green (G), and one purple (P).Abbi wins if the spinner lands on yellow or red. Bella wins if it lands on blue Claire wins if it lands on any other color.Is this a fair game? Why or why not use probabilities in your justification.

Answer 1

Abbi, Bella and Claire are playing a game with a spinner. The spinner has 5 equal-sized sections: one yellow (Y), one red (R), one blue (B), one green (G), and one purple (P).

We can find the questions below.

Step-by-step explanation

Part A: Is this a fair fame?

Answer: No

Part B: Justification

A fair game is a game in which each of the contestants should have the same likelihood of winning it, that is the game must not be biased.

The spinner has 5 equally sized sections. Abbi wins if the spinner lands on yellow or red(2 sections), Bella wins if it lands on blue( 1 section ) Claire wins if it lands on any other color(2 sections).

Therefore, the probability of each person winning becomes

`\begin{gathered} pr(win)=\frac{Number\text{ }of\text{ }sections}{Total\text{ number of sections}} \\ Pr(Abbi)=(2)/(5) \\ Pr(Bella)=(1)/(5) \\ Pr(Claire)=(2)/(5) \end{gathered}`

Since the probabilities are not equal for each of the contestants, therefore, it is justified that the game is not a fair game.