Exam 4: Basic Probability

If A and B cannot occur at the same time they are called mutually exclusive.

If P(A and B) = 1, then A and B must be collectively exhaustive.

The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is kept within budget or the campaign will increase sales is:

If event A and event B cannot occur at the same time, then events A and B are said to be

TABLE 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. You buy a single ticket. -Referring to Table 4-7, the probability that you win at least $100.00 is ________.

TABLE 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 Table 4-4, the probability a randomly selected patron is a female who prefers soda is ________.

TABLE 4-8 According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen, sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30% and 20%. -Referring to Table 4-8, what percentage of the students live in a dormitory?

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that house sales will increase but interest rates will not during the next 6 months is:

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closing price. Based on the closing price of the stock collected over the last month, 25% of the days the closing price was higher than previous day's closing price, 45% was lower than previous day's and 30% was the same as previous day's. Based on this information, the probability that tomorrow's closing price will be higher than today's is 25%. This is an example of using which of the following probability approach?

The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is married and has a college degree is:

TABLE 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. -Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm and also went bar hopping the weekend before the midterm?

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

TABLE 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 Table 4-9, if a randomly selected company is a large company, what is the probability that it offered stock options to their board members?

TABLE 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 Table 4-10, what is the probability that a randomly selected worker is not black and had not claimed bias?

TABLE 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. -Referring to Table 4-2, what is the probability that a randomly selected student who went bar hopping will do well on the midterm?

TABLE 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 Table 4-10, what is the probability that a randomly selected worker is black and had not claimed bias?

TABLE 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 Table 4-4, suppose a randomly selected patron prefers soda. Then the probability the patron is a male is ________.

TABLE 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 Table 4-6, if a randomly selected student has passed the ELM, the probability the student is from out-of-state is ________.

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The probability that the residents of a household do not own 2 cars and have an income over $50,000 a year is:

If two events are collectively exhaustive, what is the probability that one or the other occurs?