Q1. (a) What is the probability of exactly no heads in tossing a coin two times.(b) Consider the following two-way classification table of employee responses on smokingstatus in a company.Smoking statusGenderYesNoTotalMale156075Female20252080100TotalCompute the following probabilities:(i)P(Female |Yes)(ii)P(Yes and No)

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Answered: Q1. (a) What is the probability of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Given the new fad of health consciousness, a random sample of 400 college students was asked what their preferred type of drink was and whether they took regular or sugar free. The following table gives a two-way classification of the responses. Regular Sugar free TOTALS Juice 210 95 305 Iced Coffee 75 20 95 TOTALS 285 115 400 (a) If one student is selected at random from these 400 students, find the probability that this student (i) Prefers sugar free drinks (ii) Prefers juice (iii) Prefers regular juice (iv) Prefers juice given that it is a sugar free drink. (v) Prefers iced coffee or that drinks must be sugar free. (b) Are the events 'prefers juice' and 'prefers sugar free drinks' independent? Use probabilities to state your answer.
In a certain school, the probabilities of the number of students who are reported tardy are shown in the following table: Number tardy: 2 3 4 Probability: 0.17 0.25 0.31 0.21 0.06 What is the expected number of tardies (rounded to two decimal places)?
(a) 13% of customers at the snack counter of a movie theater buy soft drinks. 42% also purchase popcorn. Among those who buy soft drinks, (i) What is the probability that a customer at the counter buys a drink and popcorn? Theaters use this type of calculation to decide which products should be bundled to appeal to Based on the probability so calculated, what is your recommendation customers. Whether to bundle the products or not? (ii) If the proportion of customer who buys popcorn is 57% . Then find the probability that a customer will buy a popcorn or a soft drink?
3. Some parts of California are particularly earthquake prone. Suppose that in one metropolitan area, 25% of homeowners are insured against earthquake damage. Four homeowners are to be selected at random. Let Y be the number among the four that have earthquake insurance. (a) Find the probability distribution of Y. (b) Draw the corresponding probability histogram. (c) What is the most likely value for Y? (d) What is the probability that at least two of the four selected have earthquake insurance?
Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student . A summary of their responses follows. Business Engineering Other Totals Full-Time 352 197 251 800 Part-Time 150 161 194 505 Totals 502 358 445 1305 Develop a joint probability table for these Use the marginal probabilities of undergraduate major (business, engineering, or other) to comment on which undergraduate major produces the most potential MBA If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate engineering major? If a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree? Let A denote the event that the student intends to attend classes full-time in…
A sample of 150 plastic panels was selected and tested for shock resistance and scratch resistance. The results are summarized in the Table 4 below. Table 4: Total number of shock and scratch resistance Scratch(high) Resistance(low) Shock(high) 0.42 0.18 Resistance(low) 0.26 0.14 (a) Find the probability: i. the panel has shock(high) resistance(low). ii. the panel has scratch(high) resistance(low). i. the panel has low resistance given that high shock resistance.
Canada has two official languages, English and French. Choose a Canadian at random and ask, "What is your mother tongue?" Here is the distribution of responses, combining many separate languages from the broad Asian/Pacific region. Language English French Asian/Pacific Other Probability 0.58 0.23 0.05 ? (a) What probability should replace "?" in the distribution? (b) What is the probability that a Canadian's mother tongue is not English?
The table below shows the results of a survey that asked 1058 adults from a certain country if they favored or opposed a tax to fund education. A person is selected at random. Complete parts (a) through (c). Support Oppose Unsure Total Males 154 327 490 Females 243 293 32 568 Total 397 620 41 1058 (a) Find the probability that the person opposed the tax or is female. P(opposed the tax or is female) = 0.846 (Round to the nearest thousandth as needed.) (b) Find the probability that the person supports the tax or is male. P(supports the tax or is male) = 0.693 (Round to the nearest thousandth as needed.) (c) Find the probability that the person is not unsure or is female. P(is not unsure or is female) = Incorre (Round to the nearest thousandth as needed.)
The table below is based on the data at the beginning of this chapter and shows the probability of the next book requested falling into each of the three categories listed, assuming that each book is equally likely to be requested. Category of book Typical numbers Probability On the shelves (S) 20000 0.25 Out on loan (L) 44000 0.55 Unauthorised loan (U) 16000 0.20 Total (S + L + U) 80 000 1 What is the probability that a randomly requested book is either out on loan or on unauthorised loan (i.e. that it is not available)?
The contingency table below shows the results of a survey of video viewing habits by age. Video Viewing Platform Preferred Viewer Age 18 to 34 35 to 54 55+ Column Total Probability Mobile/Laptop Device 31 96 Probability 46 TV Screen 33 9 12 54 Row Total 64 18 298 Find the following probabilities or percentages: (a) Probability that a viewer is aged 18 to 34. (Round your answer to 2 decimal places.) 18 100 (b) Probability that a viewer prefers watching videos on a TV screen. (Round your answer to 2 decimal places.)
Luisa is a manager at a pet insurance company with many customers. Sixty percent of the company's customers filed claims in the past year. Luisa will randomly select 12 customers from all the company's customers. Assuming the customers selected are independent of each other, which of the following is closest to the probability that more than 2 of the 12 customers sampled did not file claims in the past year? (A) 0.003 (B) 0.400 (C) 0.917 (D) 0.997 (E) 0.999

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