# Intro to Probability: Golf Club, Randomly Selected Member (Math Problem Sample)

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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.**

- In a poll, respondents were asked if they have traveled to Europe. 68 respondents indicated that they
traveled to Europe and 124 respondents said that they*have*traveled to Europe. If one of these respondents is randomly selected, what is the probability of getting someone who*have not*traveled to Europe?*has* - 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.

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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