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Chapter 3: Q. 23 (page 216)

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 red, you don鈥檛 get a prize. What is P(R)?

Short Answer

Expert verified

The value ofP(R)=0.5.

Step by step solution

01

Given

The color wheel below is included in the question.

02

Concept used

Probabilityisametricfordetermininghowcertainweareoftheresultsofacertainexperiment.
Theprobabilityiscalculatedusingthefollowingformula:

Probability =Fanorable number of casesTotal 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="1648043432096" {HT,TH], soP(A)=24=0.5.

03

Calculation

Let B= be the landing event on blue.
Let's say the occurrence of landing on red is R=.
Let the event of landing on green be 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 red.
As a result, the favorable number of instances for landing on red is 4, and the overall number of cases is 8.
As a result, the likelihood of a dart landing on red is:localid="1648043445973" P(R)=48=12=0.5

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