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Chapter 5: Q. 70. (page 330)

Mac or PC? A recent census at a major university revealed that 60% of its students mainly used Macs. The rest mainly used PCs. At the time of the census, 67% of the school鈥檚 students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students and used a Mac as their main computer. Suppose we select a student at random from among those who were part of the census and learn that the person mainly uses a Mac. Find the probability that the person is a graduate student.

Short Answer

Expert verified

The probability that the randomly selected person is a graduate student is approx0.3833.

Step by step solution

01

Given information

60%of the students mainly use MACs.

67%are undergraduates.

23%are graduates who mainly use a MAC.

02

Explanation

G: for graduates

U: for undergraduates

MAC: for MAC users

The probabilities are as follows:

Probability for MAC users,

P(MAC)=0.60

Undergraduates' probability,

P(U)=0.67

Graduates and MAC users have a higher chance of succeeding.

P(GandMAC)=0.23

Because the person who was chosen at random primarily uses a Mac.

Use the conditional probability formula:

P(G鈭�MAC)=P(Gand MAC)P(MAC)=0.230.60=2360鈮�0.3833

Therefore, the probability that the randomly selected person is a graduate student is approx0.3833.

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Most popular questions from this chapter

Butter side down Refer to the preceding exercise. Maria decides to test this

probability and drops 10 pieces of toast from a 2.5-foot table. Only 4of them land butter

side down. Maria wants to perform a simulation to estimate the probability that 4or

fewer pieces of toast out of 10would land butter side down if the researchers鈥� 0.81

probability value is correct.

a. Describe how you would use a table of random digits to perform the simulation.

b. Perform 3trials of the simulation using the random digits given. Copy the digits onto

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29077
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c. The dotplot displays the results of 50 simulated trials of dropping 10pieces of toast.

Is there convincing evidence that the researchers鈥� 0.81probability value is incorrect?

Explain your answer.

Ten percent of U.S. households contain 5or more people. You want to simulate choosing a household at random and recording 鈥淵es鈥� if it contains 5or more people. Which of these is a correct assignment of digits for this simulation?

a.Odd=Yes;Even=No

b.0=Yes;1鈥�9=No

c.0鈭�5=Yes;6鈭�9=No

d.0鈭�4=Yes;5鈭�9=No

e. None of these

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a. What must be the probability that a randomly chosen young adult has some education beyond high school but does not have a bachelor鈥檚 degree? Why?

b. Find the probability that the young adult completed high school. Which probability rule did you use to find the answer?

c. Find the probability that the young adult has further education beyond high school. Which probability rule did you use to find the answer?

Foreign-language studyChoose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of results:

a. What鈥檚 the probability that the student is studying a language other than English?

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studying some language other than English?

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the rest were Democrats or Independents. Twenty-one percent of the senators were

females, and 47%of the senators were male Republicans. Suppose we select one of these

senators at random. Define events R: is a Republican and M: is male.

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b. Consider the event that the randomly selected senator is a female Democrat or

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