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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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Most popular questions from this chapter

Use the following information to answer the next 12exercises. The graph shown is based on more than localid="1648902668215">170,000interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score.

If we know an Emotional Health Index Score is 81.5 or more, what is the probability that it is 82.7.

Roll a fair, six-sided die. Let A = a prime number of dots is rolled. Let B = an odd number of dots is rolled. Then A = {2, 3, 5} and B = {1, 3, 5}. Therefore, A AND B = {3, 5}. A OR B = {1, 2, 3, 5}. The sample space for rolling a fair die is S = {1, 2, 3, 4, 5, 6}. Draw a Venn diagram representing this situation.

When the Euro coin was introduced in 2002, two math professors had their statistics students test whether the Belgian one Euro coin was a fair coin. They spun the coin rather than tossing it and found that out of 250spins,140showed a head (event H) while 110showed a tail (event T). On that basis, they claimed that it is not a fair coin.

a. Based on the given data, find P(H) and P(T).

b. Use a tree to find the probabilities of each possible outcome for the experiment of tossing the coin twice.

c. Use the tree to find the probability of obtaining exactly one head in two tosses of the coin.

d. Use the tree to find the probability of obtaining at least one head

E and F are mutually exclusive events. P(E) = 0.4; P(F) = 0.5. Find P(E鈭).

Write the symbols for the probability that of all the outfielders, a player is not a great hitter.
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