Practice Questions Chapter 41 Male And Female Students

Practice Questions Chapter 41 Male And Female Students At A High Scho

Practice Questions Chapter . Male and Female students at a high school were surveyed about their career preferences. The data are shown in the table below. Doctor Engineer Other Total Male Female Total a. What is the probability that a randomly selected student wants to be an Engineer? b. What is the probability that a randomly selected student is a Female and wants to be a Doctor? c. What is the probability that a randomly selected student wants to be a Doctor or Male? d. What is the probability that a randomly selected student wants to be an Engineer given that he is Male? 2. The contingency table below shows the statistics for 300 students distributed over three different majors (business, management and finance). If a student is selected at random, Major Freshman Junior Sophomore Total Business Management Finance Total a. What is the probability that he/she is Freshman and he/she is a Finance major? b. What is the probability that he/she is Freshman and he/she is not a Finance major? c. What is the probability that he/she is a Management major or he/she is a Sophomore? d. What is the probability that he/she is a Management major given that he/she is a Junior? 3. A survey among 250 Junior and Senior students in a particular university in Kuwait resulted in the following information. If randomly a student is selected, Year Mathematics Economics Accounting Total Junior Senior Total a. What is the probability that that student is taking Mathematics? b. What is the probability that that student is senior and taking Accounting? c. What is the probability that that student is senior or taking Accounting? d. What is the probability that that student is Junior given that he/she is taking Economics? 4. A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their compensation packages. For small companies, 43 of the 180 surveyed indicated that they offer stock options as part of their compensation packages to their board members. a. Complete the following contingency table. Company Size Large Small Total Stock Options Yes No Total b. What is the probability that the company offered stock options to their board members? c. What is the probability that the company is small or offered stock options to their board members? d. What is the probability that a randomly selected company offered stock options to their board members given that it is a large company? 5. A sample of 300 adults is selected. The contingency table below shows their registration status and their preferred source of information on current events. If an adult is selected at random, Television Newspapers Radio Internet Total Registered voter Not registered voter Total a. What is the probability that he/she prefers to get his/her current information from the Internet? b. What is the probability that he/she is a registered voter? c. What is the probability that he/she is a registered voter and prefers to get his/her current information from the television? d. What is the probability that he/she is Not a registered voter and prefers to get his/her current information from the Newspapers? e. What is the probability that he/she is a registered voter given that he/she prefers to get his/her current information from the Radio? 6. A quality control inspector is checking a sample of lightbulbs for defects. The table summarizes the results. If one of these light bulbs is selected at random Good Defective Total Low watts Medium watts High Total a. What is the probability that the light bulb is defective? b. What is the probability that the light bulb is Defective or high watt? c. What is the probability that the light bulb is good or low watt? d. What is the probability that the light bulb is good given that it is low watts? 7. Suppose that patrons of a restaurant were asked whether they preferred water or whether they preferred soda (S). 70% of the patrons are males. 15% of the females (F) preferred soda. 80% of the males (M) preferred water (W). Total Total a. Find the probability that a randomly selected patron prefers soda P (S). b. Find the probability that we randomly selected patron is a male given that he prefers water, 8. An airport screens bags for Forbidden Items (FI), and an alarm is supposed to be triggered when a FI is detected. Suppose that 5% of bags contain FI. If a bag contains a FI, there is a 98% chance that it triggers the alarm. If a bag doesn't contain a FI, there is an 8% chance that it triggers the alarm. a. Draw a contingency table? Contain FI Don’t contain FI Total Trigger the alarm Don’t trigger the alarm Total b. Find the probability that a randomly selected bag contains a FI and triggers the alarm c. Given that a randomly chosen bag triggers the alarm, what is the probability that it contains a FI? Total Total 9. Assume that a person comes to a movie on time or late. If a person comes the movie on time, there is 80% chance that he will like the movie. If he comes late, there is a 40% chance that he will not like the movie. If 30% people are late based on History; a. What is the probability that a randomly selected person liked the movie? b. What is the probability that a randomly selected person was late and did not like the movie? c. What is the probability that a randomly selected person was late given that he liked the movie? 10. Students in a certain community were surveyed. Among these students, 60% indicated that they have a laptop. Of those that have a laptop, 90% have a smartphone. Of those that do not own a laptop, 30% have a smartphone. a. Fill in the contingency table Has smartphone Does not have smartphone Total Has laptop Does not have a laptop Total b. If a student is chosen at random, what is the probability that the student has a laptop? c. If a student is chosen at random, what is the probability that the student has a laptop and smartphone? d. If a student is chosen at random, what is the probability that the student does not have a laptop and has a smartphone? e. What is the probability that the student has a laptop given that he/she has a smartphone? 11. At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out-of-state. All students must take and pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the northerners have passed the ELM, and 90% of the out-of-staters have passed. Total Total a. What is the probability that a randomly selected student is from northern Texas and didn’t pass the ELM? b. What is the probability that a randomly selected student has passed the ELM? c. What is the probability that a randomly selected student is from southern Texas given that he passed the ELM? Practice Questions on Counting rules 12. a. A simple survey consists of three multiple choice questions. The first question has 3 possible answers, the second has 4 possible answers and the third has 5 possible answers. What is the total number of different ways in which this survey could be completed? b. How many ways can a company select 3 candidates to interview from a short list of 15 ? 13. a. Of five letters (A, B, C, D, E), three letters are to be selected at random. How many possible selections are there? b. An experiments consists of three steps. There are 5 possible results in the first step, 4 possible results on the second step and 3 possible results on the third step. How many total number of experiment outcome are there? 14. a. A student has 6 different books. In how many ways he can arrange these books on a bookshelf? b. A student has 6 different books, but there is room for only 4 books on the shelf, how many ways are there of placing 4 books into the shelf? 15. An inspection team of 3 lawyers is to be chosen from a candidate pool of 7 lawyers. How many different ways can this team of 3 be formed? 16. You are planning to register in 2 Science courses and 3 Math courses next semester. Currently, there are 5 open Science courses and 6 open Math courses. a. How many different ways can you choose 2 Science courses? b. How many different ways can you choose 3 Math courses? c. How many different ways can you choose 2 Science courses and 3 Math courses? d. If you have to take Basic calculus as part of your math courses, how many different ways can you choose 2 Science courses and 3 Math courses? 17. a. A team is being formed that includes 11 different people. There are different positions on the team. How many different ways are there to assign the 11 people to the 11 positions? b. A student has 9 course books that she would like to place in her backpack. However, she only has room for 3 books. Regardless of the arrangement, how many ways are there she can select 3 books into her backpack? 18. Suppose that you roll a die 2 times. a. Find the number of possible outcomes and list them. b. What is the probability that the first die is 3; and the second die is 4? c. What is the probability that you get one 3 and one 4? d. What is the probability that their sum is more than 9? 19. Suppose that you toss a fair coin 3 times. a. List all possible outcomes. b. What is the probability that all three are tails? c. What is the probability that only one of them is Head? d. What is the probability that at least one of them is Head? 20. There are 6 doctors and 8 nurses in a clinic. a. How many different ways can you choose 2 doctors? b. How many different ways can you choose 3 Nurses? c. How many different ways can you choose 2 doctors and 3 nurses? d. If the specialist nurse Mrs. X has to be in the Group of 3 Nurses, in how many different ways you can choose 2 doctors and 3 nurses? e. If you randomly choose 5 persons, what is the probability that there are 2 doctors and 3 nurses? 21. If 5 friends (A, B, C, D, E) sit in a row a. How many different ways can they sit? b. How many different ways can they sit such that A sits next to D? c. How many different ways can they sit such that A & D do not sit next to each other? Practice Questions Chapter . Male and Female students at a high school were surveyed about their career preferences. The data are shown in the table below. Doctor Engineer Other Total Male Female Total a. What is the probability that a randomly selected student wants to be an Engineer? b. What is the probability that a randomly selected student is a Female and wants to be a Doctor? c. What is the probability that a randomly selected student wants to be a Doctor or Male? d. What is the probability that a randomly selected student wants to be an Engineer given that he is Male?

Paper For Above instruction

The comprehensive analysis of probability in various contexts demonstrates its fundamental role in decision-making, risk assessment, and understanding uncertainties in everyday and professional situations. This paper explores several probability problems drawn from diverse scenarios including student career choices, company statistics, community engagement, security screening, and recreational activities. We will elucidate the concepts of basic probability, conditional probability, joint probability, and the application of counting rules to determine likelihoods in complex situations.

Introduction

Probability theory provides the mathematical framework to quantify uncertainty, allowing us to assess the chance of specific events occurring. Its applications range from academic settings, such as evaluating student data, to real-world scenarios like security checks and market research. Understanding how to compute probabilities based on given data enhances analytical skills essential for decision-making processes.

Probability in Student Career Preferences

Consider a high school survey where the career aspirations of male and female students are analyzed. Suppose the total sample includes students who wish to be doctors, engineers, or other professions. To find the probability that a randomly selected student desires to be an engineer, we divide the number of students who prefer engineering by the total number of students surveyed. For instance, if 50 students out of 200 intend to become engineers, the probability is 50/200 = 0.25, or 25%. Similarly, calculating the probability for other combinations involves understanding joint and conditional probabilities, requiring the integration of data from the contingency table.

For example, the probability that a student is female and wants to be a doctor is calculated by dividing the number of female students who want to be doctors by the total sample. Such analysis assists in demographic studies and targeted career counseling.

Company and Organizational Data Analysis

Data from corporate surveys about stock options reveal insights into employee compensation packages based on company size. By constructing a contingency table, we estimate probabilities such as the chance a company offers stock options. For example, if 43 large companies and 43 small companies offer stock options, totaling 86, the probability that a randomly selected company offers stock options is 86 divided by total companies surveyed. Conditional probabilities, such as the likelihood a company offers stock options given it is large, are computed using Bayes’ theorem, demonstrating the importance of understanding conditional probability in classification problems.

Community Engagement and Political Involvement

Community participation is vital for fostering awareness and activism for causes such as social justice, environmental issues, or political movements. Low participation levels can be analyzed through surveys indicating the proportion of residents attending events or engaging in activism. Promoting awareness and social media campaigns are effective strategies to increase participation, which are fundamentally probabilistic in assessing the impact of interventions and outreach efforts.

Security Screening and Risk Assessment

Analyzing data related to airport security, such as the probability of bags containing forbidden items and triggering alarms, involves constructing contingency tables. For example, with known rates of forbidden items (5%), alert trigger probabilities in case of actual forbidden items (98%), and false alarms (8%), we can compute the probability that a triggered alarm indicates a bag truly contains forbidden items using Bayes’ theorem. This application emphasizes the importance of probabilistic reasoning in safety and security protocols.

Recreational and Behavioral Studies

Studies involving random events like dice rolls, coin tosses, or seating arrangements exemplify counting principles and probability calculations. For example, determining the probability of rolling a specific number sequence in two dice outcomes, or calculating the likelihood of specific patterns in coin tosses, demonstrates fundamental combinatorial principles. These explorations highlight how understanding permutations and combinations underpin probability computations in recreational activities.

Conclusion

Probability theory is indispensable across various domains, offering tools to quantify uncertainty and make informed decisions. From analyzing student preferences to assessing security risks, the concepts of probability, conditional probability, and counting rules form the backbone of data-driven decision-making. Mastery of these principles enhances analytical capabilities in academic, professional, and everyday contexts, enabling individuals to navigate uncertainties effectively and ethically.

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