Exam 4: Basic Probability

Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5.Then P (A orB) = .

SCENARIO 4-9 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 non-cash compensation packages.For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. -Referring to Scenario 4-9, if a company is selected at random, what is the probability that the company offered stock options to their board members?

SCENARIO 4-2 An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm.The following result was obtained. Did Well on Midterm Did Poorly on Midterm Studying for Exam 80 20 Went Bar Hopping 30 70 -Referring to Scenario 4-2, what is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the midterm?

SCENARIO 4-12 Jake woke up late in the morning on the day that he has to go to school to take an important test.He can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable motorcycle which breaks down 40% of the time.He decides to toss a fair coin to make his choice. -Referring to Scenario 4-12, if Jake, in fact, gets to the test on time, what is the probability that he rode his motorcycle?

SCENARIO 4-3 A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger and 80 preferred chicken.55 of the children preferred hamburger. -Referring to Scenario 4-3, assume we know that a person prefers hamburger.The probability that this individual is a child is .

SCENARIO 4-4 Suppose that patrons of a restaurant were asked whether they preferred water or whether they preferred soda.70% said that they preferred water.60% of the patrons were male.80% of the males preferred water. -Referring to Scenario 4-4, the probability a randomly selected patron is a female who prefers water is .

SCENARIO 4-6 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 the ELM. -Referring to Scenario 4-6, the probability that a randomly selected student is not from southernTexas and has not passed the ELM is .

SCENARIO 4-6 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 the ELM. -Referring to Scenario 4-6, the probability that a randomly selected student has passed the ELMis _.

An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of gain.It is an ethical practice to explain to the clienteles what the basis of her probability estimate is.

If two events are mutually exclusive, what is the probability that both occur at the same time?

SCENARIO 4-10 Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were black and 10% are other races.Given that a worker was white, the probability that the worker had claimed bias was 30%.Given that a worker was black, the probability that the worker had claimed bias was 40%.Given that a worker was other race, the probability that the worker had claimed bias was 0%. -Referring to Scenario 4-10, what is the probability that a randomly selected worker is white and had claimed bias?