/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 49 Mac or PC? A recent census at a ... [FREE SOLUTION] | 91影视

91影视

Mac or PC? A recent census at a major university revealed that60%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. Define events G: is a graduate student and M: primarily uses a Mac.

a. Find P(G 鈭 M). Interpret this value in context.

b. Consider the event that the randomly selected student is an undergraduate student and

primarily uses a PC. Write this event in symbolic form and find its probability.

Short Answer

Expert verified

(a) The value of PGMis0.70.

(b) The symbolic form is PUPand the probability is0.30.

Step by step solution

01

Part (a) Step 1: Given Information

We are given the values of the students who are undergraduate and who use Macs and also those who are both graduate and use Macs, and we have to find out the probability of those who are either graduate or use Macs.

02

Part (a) Step 2: Explanation

Applying the union rule of probability

which isPAB=P(A)+P(B)+P(AB),

Here, P (G)=1-PU=1-0.67=0.33, P (M)=0.60and P(GM)=0.23

Put all the values in the rule.

We get PGM=0.33+0.60-0.23=0.70

Hence, the probability of those who are graduates or using Macs is0.70

03

Part (b) Step 1: Given Information

We are given the values of the students who are undergraduate and who use Macs and also those who are both graduate and use Macs, and we have to find out the probability of those who are graduate or use Macs.

04

Part (b) Step 2: Explanation

Applying the union rule of probability,

which isPAB=P(A)+P(B)+P(AB)

Here, the probability of students who are undergraduates and use primarily PCS is denoted by PUP. Now, to find its value,

P(U)=0.67, P(P)=1-P(M)=1-0.60=0.40

and P(UP)=1-0.23=0.77

Put all the values in the union rules.

we getPUP=0.67+0.40-0.77=0.30.

Hence, the probability is0.30.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

AARP, and Medicare (4.1) To find out what proportion of Americans support proposed

Medicare legislation to help pay medical costs, the AARP conducted a survey of their

members (people over age 50 who pay membership dues). One of the questions was:

鈥淓ven if this plan won鈥檛 affect you personally either way, do you think it should be passed

so that people with low incomes or people with high drug costs can be helped?鈥 Of the

respondents, 75% answered 鈥淵es.鈥

a. Describe how undercoverage might lead to bias in this study. Explain the likely

direction of the bias.

b. Describe how the wording of the question might lead to bias in this study. Explain the

likely direction of the bias.

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

your paper and mark directly on or above them so that someone can follow what you

did.

29077
14863
61683
47052
62224
51025
95052
90908
73592
75186
87136
95761
27102
56027
55892
33063
41842
81868

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.

In a sample of275students, 20say they are vegetarians. Of the vegetarians, 9eat both fish and eggs, 3eat eggs but not fish, and 7eat neither. Choose one of the vegetarians at

random. What is the probability that the chosen student eats fish or eggs?

a. 9/20

b. 13/20

c. 22/20

d. 9/275

e.22/275

Double fault!A professional tennis player claims to get 90%of her second serves in. In a recent match, the player missed 5of her first 20second serves. Is this a surprising result if the player鈥檚 claim is true? Assume that the player has a 0.10probability of missing each second serve. We want to carry out a simulation to estimate the probability that she would miss 5or more of her first 20second serves.

a. Describe how to use a random number generator to perform one trial of the simulation. The dot plot displays the number of second serves missed by the player out of the first 20second serves in simulated matches.

b. Explain what the dot at 6represents.

c. Use the results of the simulation to estimate the probability that the player would miss 5or more of her first 20second serves in a match.

d. Is there convincing evidence that the player misses more than 10%of her second serves? Explain your answer.

Reading the paper In a large business hotel, 40%of guests read the Los Angeles Times. Only read the Wall Street Journal. Five percent of guests read both papers. Suppose we select a hotel guest at random and record which of the two papers the person reads, if either. What鈥檚 the probability that the person reads the Los Angeles Times or the Wall Street Journal?

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.