Question

1. a game at the fair involves a wheel with seven sectors. two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue.

landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give -1 point.
a. let x = the points you have after one spin. fill out the missing values in the table.

Explanation:

Step1: Determine the values of \(X\)

The possible points are based on the color - landing rules. So \(X\) values are \(3\) (blue), \(1\) (yellow), \(0\) (purple), \(- 1\) (red).

Step2: Calculate the probabilities \(P(X)\)

• For \(X = 3\) (blue sector): There is \(1\) blue sector out of \(7\) sectors. So \(P(X = 3)=\frac{1}{7}\).
• For \(X = 1\) (yellow sectors): There are \(2\) yellow sectors out of \(7\) sectors. So \(P(X = 1)=\frac{2}{7}\).
• For \(X = 0\) (purple sectors): There are \(2\) purple sectors out of \(7\) sectors. So \(P(X = 0)=\frac{2}{7}\).
• For \(X=-1\) (red sectors): There are \(2\) red sectors out of \(7\) sectors. So \(P(X=-1)=\frac{2}{7}\).

Answer:

\(X_i\)	\(3\)	\(1\)	\(0\)	\(-1\)