1) In a batch of 20 television picture tubes, 5 are known to be defective. What is the probability that a random sample of 5 (without replacement) will result in each of the following? (75 words, or 1 paragraph)
Exactly 1 defective
Two or fewer defective
2) The board of directors for a particular company consists of 10 members, 6 of whom are loyal to the current company president and 4 of whom want to fire the president. Suppose the chair of the board (who is a loyal supporter of the current president) suggests to randomly select 4 other board members to serve on a committee to decide the president’s fate. Find the probability for the first 3 questions and explain your answer for the fourth question. (75–150 words, or 1–2 paragraphs)
What is the probability that all 5 committee members will vote to keep the president in place, if no one changes their minds?
What is the probability that a majority of the committee will vote to keep the president in place, if no one changes their minds?
What is the probability that the vote is 4 to 1 to replace the president, if no one changes their minds?
Imagine that you were the president of the company and you hoped to keep your position. Considering the various probabilities, would you consider the chair of the board’s suggestion to be in your favor or not? If the choice was yours, would you allow the suggestion to proceed?
3) Dave has just left an interview with a prospective employer. The hiring manager told Dave that she will tolerate one mistake during his first year but will fire him if he makes two mistakes. Based on Dave’s research and understanding of the job, he estimates that he will have to make five critical decisions during the year, and with his knowledge of the processes, figures that he will have about an 80% chance of making any of those five decisions correctly. Dave does not want to run any more than a 25% chance of being fired. If each of the decisions is independent of the others, should Dave risk taking the job if offered? Explain why or why not. (75 words, or 1 paragraph)