Exam 4: Basic Probability

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 two events "preferring water" and "preferring soda" are independent.

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, if a randomly selected student has not passed the ELM, the probability the student is not from northern Texas is .

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, when a randomly selected worker was not white, what is the probability that the worker had not claimed bias?

SCENARIO 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 Scenario 4-8, what is the probability that a randomly selected student is a freshman who lives in a dormitory?

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

A company has 2 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 3 times as many widgets as the older machine does.What is the probability that a randomly chosen widget produced by the company is defective?

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 who went bar hopping did well on the midterm?

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, the events "Did Well on Midterm" and "Studying for Exam" are

Selection of raffle tickets from a large bowl is an example of

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) = .

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, if a randomly selected worker had claimed bias, what is the probability that the worker is white?

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

Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P (A and B) = 0.1. $\text { Then } P ( B \mid A ) =$

When A and B are mutually exclusive, P (A or B) can be found by adding P(A) andP(B).

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 originalbudget allocation is 0.40.If the two events are independent, the probability that the cost is kept within budget and the campaign will increase sales is:

$\text { If } \mathrm { P } ( A ) = 0.4 \text { and } \mathrm { P } ( B ) = 0.6$ , then A and B must be collectively exhaustive.

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closed.Without any prior information that may affect the price of the stock tomorrow, the probability that it will close higher than today's close is 1/3.This is an example of using which of the following probability approach?

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 be0.74.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:

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, suppose a randomly selected patron is a female.Then the probability the patron prefers water is .

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 originalbudget allocation is 0.40.If the two events are independent, the probability that the cost is kept within budget or the campaign will increase sales is: