Exam 4: Basic Probability

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

A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class. How many possible ways can the team be formed which will include both of the twin brothers?

If two events are independent, what is the probability that they both occur?

Suppose A and B are independent events where P(A)= 0.4 and P(B)= 0.5. Then P(A and B)= ________.

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% were 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 white and had claimed bias?

A company has two machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces three times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is not defective?

Twelve students in a Business Statistics class are to be formed into three teams of four. How many different ways can this be done?

Suppose A and B are events where P(A)= 0.4, P(B)= 0.5, and P(A and B)= 0.1. Then P(A or B)= ________.

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, on 25% of the days the closing price was higher than previous day's closing price, on 45% of the days it was lower than previous day's closing price, and on 30% of the days it was the same as previous day's closing price. 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?

TABLE 4-1 Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: -Referring to Table 4-1, what proportion of accidents involved more than one vehicle?

TABLE 4-3 A survey is taken among customers of a fast-food restaurant to determine their 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 Table 4-3, assume we know that a person prefers hamburger. The probability that this individual is a child is ________.

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

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% were 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?

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 ________.

If P(A)= 0.4 and P(B)= 0.6, then A and B must be collectively exhaustive.

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 is the probability that a randomly selected student is a freshman who lives 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 both house sales and interest rates will increase during the next 6 months is ________.

If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur?

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 two events "preferring water" and "being a male" are independent.

According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents of a household own two cars and have an income less than or equal to $50,000 a year is ________.