Question

Use the following information to answer the next two exercises. You see a game at a local fair. You have to throw a dart at a color wheel. Each section on the color wheel is equal in area.

Let B = the event of landing on blue.

Let R = the event of landing on red.

Let G = the event of landing on green.

Let Y = the event of landing on yellow.

If you land on Y, you get the biggest prize. Find P(Y).

Short answer

The solution is$$\begin{gathered} P\left(Y\right)=\frac{1}{8} \\ =0.125 \end{gathered}$$

Step-by-step solution

Given

The color wheel below is included in the question.

Concept used

Probabilityisametricfordetermininghowcertainweareoftheresultsofacertainexperiment.

Theprobabilityiscalculatedusingthefollowingformula:

Probability $=\frac{\text{Fanorable number of cases}}{\text{Total number of cases}}$

For example, if we flip a coin two times, the sample space associated with this random experiment is $\{HH,HT,TH,TT]$where T tails and H heads. Let's suppose A getting one tail. There are two outcomes which favors the event A

localid="1648043374340" $$\begin{gathered} \{HT,TH]\text{, so}P\left(A\right)=\frac{2}{4} \\ =0.5\text{.} \end{gathered}$$

Calculation

Let$B=$bethelandingeventonblue.

Let's say the occurrence of landing on red is R=.

Assume that the event of landing on green is G=.

Assume that the event of landing on yellow is Y=.

We can see from the wheel that there are four different ways to land a dart on a red color, two ways to land a dart on a blue color, one way to land a dart on a green color, and one way to land a dart on a yellow color.

We must calculate the likelihood of a dart landing on yellow.

As a result, the favorable number of instances for landing on yellow is 1 and the overall number of cases is 8.

As a result, the likelihood of a dart landing on yellow is: $$\begin{gathered} P\left(Y\right)=\frac{1}{8} \\ =0.125 \end{gathered}$$