given the spinner below in which all regions are equal, which of the following point scales would result in…

given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game? the odd numbered regions will add one point. the even numbered regions lose one point. red will add one point. any other color will lose one point. a number less than or equal to 3 will add one point. a 4 will lose two points.

given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game? the odd numbered regions will add one point. the even numbered regions lose one point. red will add one point. any other color will lose one point. a number less than or equal to 3 will add one point. a 4 will lose two points.

Answer

Explanation:

Step1: Calculate expected - value for first option

The odd - numbered regions are 1 and 3, and the even - numbered regions are 2 and 4. The probability of landing on an odd - numbered region $P(O)=\frac{2}{4}=\frac{1}{2}$, and the probability of landing on an even - numbered region $P(E)=\frac{2}{4}=\frac{1}{2}$. The expected value $E_1$ is $E_1=\frac{1}{2}\times1+\frac{1}{2}\times(- 1)=0$.

Step2: Calculate expected - value for second option

The probability of landing on red $P(R)=\frac{1}{4}$, and the probability of landing on non - red $P(NR)=\frac{3}{4}$. The expected value $E_2$ is $E_2=\frac{1}{4}\times1+\frac{3}{4}\times(-1)=\frac{1 - 3}{4}=-\frac{1}{2}$.

Step3: Calculate expected - value for third option

The numbers less than or equal to 3 are 1, 2, 3. The probability of landing on a number less than or equal to 3 $P(\leq3)=\frac{3}{4}$, and the probability of landing on 4 $P(4)=\frac{1}{4}$. The expected value $E_3$ is $E_3=\frac{3}{4}\times1+\frac{1}{4}\times(-2)=\frac{3-2}{4}=\frac{1}{4}$.

Answer:

A number less than or equal to 3 will add one point. A 4 will lose two points.