A research team conducted a study showing that approximately 20% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.) a. At least 1 tie is too tight b. more than 2 ties are too tight c. no tie is too tight

At a company, the employees were surveyed and classified according to their level of education and whether they smoked or not. The data are shown in the table.   High school graduate College graduate Smoke 09 19 Do not Smoke 17 25 If an employee is selected at random, find the following probabilities. (Round your answers to three decimal places) a. Employee smokes and is a college graduate.  b. Employee smokes or is a college graduate.  c. Employee smokes, given that he or she graduated from college.  d. Employee is a college graduate, given that he or she smokes.

Sociologists say that 85% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that seven married women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. Round your answers to three decimal places.)   (a) All of them dislike their mother-in-law. (b) None of them dislike their mother-in-law. (c) At least five of them dislike their mother-in-law. (d) No more than four of them dislike their mother-in-law.

A recent survey by the New Statesman on British social attitudes asked respondents if they believe that inequality is too large. The survey found that 65% of the respondents do believe inequality is too large. In a sample of six British citizens, what is the probability that two believe inequality is too large? If required, round your answer to four decimal places.f (2) = In a sample of six British citizens, what is the probability that at least two respondents believe that inequality is too large? If required, round your interim calculations and final answer to four decimal places.P (at least 2) = In a sample of four British citizens, what is the probability that none believe inequality is too large? If required, round your answer to four decimal places.f (0) =

A company retains a psychologist to assess whether job applicants are suited for assembly‑line work. The psychologist classifies applicants as one of ?A (well suited), ?B (marginal), or ?C (not suited). The company is concerned about the group ?D , where an employee leaves the company within a year of being hired. Data on all people hired in the past five years give the probabilities shown. ?(?)=0.4P(A)=0.4 ?(?)=0.3P(B)=0.3 ?(?)=0.3P(C)=0.3 ?(? and ?)=0.1P(A and D)=0.1 ?(? and ?)=0.1P(B and D)=0.1 ?(? and ?)=0.2P(C and D)=0.2   Select the correct Venn diagram of the events ?,?,?,A,B,C, and ?D showing the probabilities of all combinations of psychological assessment and leaving (or not) within a year.