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10 pages/≈2750 words
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APA
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Mathematics & Economics
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Math Problem
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Intro to Probability: Golf Club, Randomly Selected Member (Math Problem Sample)

Instructions:

Please pay close attention to the BOLD writing all work must be shown. All attached background and assignment information will be added.

By submitting this assignment, you affirm that it contains all original work, and that you affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Answer the following problems showing your work and explaining (or analyzing) your results.

  1. In a poll, respondents were asked if they have traveled to Europe. 68 respondents indicated that they have traveled to Europe and 124 respondents said that they have not traveled to Europe. If one of these respondents is randomly selected, what is the probability of getting someone who has traveled to Europe? 
  2. The data set represents the income levels of the members of a golf club. Find the probability that a randomly selected member earns at least $100,000.
source..
Content:

Introduction to Probability
Name
Institution
Introduction to Probability
1 In a poll, respondents were asked if they have traveled to Europe. 68 respondents indicated that they have traveled to Europe and 124 respondents said that they have not traveled to Europe. If one of these respondents is randomly selected, what is the probability of getting someone who has traveled to Europe? 
Solution
The total number of respondents = (68+124) =192
Those who have travelled to Europe =68
Those who have not travelled to Europe =124
P (Travelled to Europe) = No.of respondents who have travelled to EuropeTotal no.of respondets
P (Travelled to Europe) = 68192 = 0.3542
Therefore, the probability of randomly selecting a respondent who have travelled to Europe is 0.3542
2 The data set represents the income levels of the members of a golf club. Find the probability that a randomly selected member earns at least $100,000.
INCOME (in thousands of dollars)
 98   102   83   140   201   96   74   109   163   210
 81   104   134   158   128   107   87   79   91   121
Solution
The number of members earning 100,000 or more = 12 (those in yellow highlight)
The total number of members = 20
P (a member earning at least 100,000) = Number of those earning 100,000 or moreTotal number of all members
P (X≥100,000) = Number of those earning 100,000 or moreTotal number of all members = 1220 = 0.6
Therefore, the probability that a member selected randomly earns at least 100,000 is 0.6
1 A poll was taken to determine the birthplace of a class of college students. Below is a chart of the results.
1 What is the probability that a female student was born in Orlando?
Solution
The total number of students = (10+16+5+12+7+9) =59
The number of female student from Orlando = 12
P (female student from Orlando) = Total number of female students from OrlandoTotal number of students = 1259 = 0.2034
2 What is the probability that a male student was born in Miami?
Solution
Number of male students born in Miami = 7
Total number of students =59 (from previous calculation)
P (male student from Miami) = Total number of male students from MiamiTotal number of students =759 =0.119
3 What is the probability that a student was born in Jacksonville?
Solution
Total number of students from Jacksonville = (10+16) = 26
Total number of students in class =59 (from previous calculation)
P (student from Jacksonville) = Total number of students from JacksonvilleTotal number of students =2659 = 0.4407
1 Of the 538 people who had an annual check-up at a doctor’s office, 215 had high blood pressure. Estimate the probability that the next person who has a check-up will have high blood pressure.
Solution
Number of people who had high blood pressure =215
Total number of people who were tested = 538
P (any person tested will have high blood pressure) = Number of people who had H.B.PTotal number of people tested =215538 = 0.3996
Therefore, the chance of the next person to have high blood pressure is at 0.3996.
2 Find the probability of correctly answering the first 4 questions on a multiple choice test using random guessing. Each question has 3 possible answers.
Solution
P (picking any right answer) =Chances of picking a right answerTotal possible answers
P (picking a right answer from the first question) = 13
P (picking a right answer from the second question) = 13
P (picking a right answer from the third question) = 13
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