Exam 4: Basic Probability

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:

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, if a randomly selected student does not live in the dormitory, what is the probability that the student is a junior or a senior?

An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women and 7 men.How many different ways can this team of 5 be formed?

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 black and had not claimed bias or is white and has claimed bias?

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

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 own 2 cars and have an income over $50,000 a year is:

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 "Did Poorly on Midterm" are

SCENARIO 4-11 A sample of 300 adults is selected.The contingency table below shows their registration status and their preferred source of information on current events. Preferred source of information Television Newspapers Radio Internet Voting registration status Registered 45 30 45 36 Not registered 35 44 45 20 -Referring to Scenario 4-11, if a randomly selected adult is a registered voter, what is the probability that he/she prefers to get his/her current information from the newspapers?

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 is late to the test, what is the probability that he rode his motorcycle?

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 is small to mid-sized or offered stock options to their board members?

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 events increase in house sales and no increase in house sales in the next6 months are

SCENARIO 4-11 A sample of 300 adults is selected.The contingency table below shows their registration status and their preferred source of information on current events. Preferred source of information Television Newspapers Radio Internet Voting registration status Registered 45 30 45 36 Not registered 35 44 45 20 -Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter and prefers to get his/her current information from the television?

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 neither house sales nor interest rates will increase during the next 6 months 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 and the campaign will increase sales is:

You know that the probability of a randomly selected student will cheat on an exam is 1%.You also know that the probability of a randomly selected student will cheat on an exam knowing that his/her fellow classmate is cheating on the exam is also 1%.Which of the following is true about the event of "the randomly selected student cheating on an exam" and "his/her classmate is cheating on the exam"?

When using the general multiplication rule, P (A and B) is equal to

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 from southern Texas is .

SCENARIO 4-1 Mothers Against Drunk Driving is a very visible group whose 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: Number of Vehicles involved Did alcohol play a role? Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Scenario 4-1, given that 3 vehicles were involved, what proportion of accidents involved alcohol? a) $20 / 30$ or $66.67 \%$ b) $20 / 50$ or $40 \%$ c) $20 / 170$ or $11.77 \%$ d) $20 / 400$ or $5 \%$

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

A survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment) on a certain date in the past. Interest Rate 3.20\% to 3.29\% 3.30\% to 3.40\% to 3.39\% 3.50\% to 3.59\% 3.60\% and above Probability 0.12 0.23 0.24 0.35 0.06 If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 3.49%?