Exam 4: Basic Probability

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

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 not claimed bias,what is the probability that the worker is white?

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 4-4 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 prefers soda 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 two events "preferring water" and "preferring soda" are independent.

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:

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. -Referring to Scenario 4-11,if an adult is selected at random,what is the probability that he/she is a registered voter?

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 percentage of the students live in a dormitory?

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 took the bus?

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 someone from northern Texas who has not passed the ELM 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 original budget allocation is 0.40.If the two events are independent,the probability that the cost is not kept within budget or the campaign will not increase sales is:

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?

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 meaning of probability 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,if a randomly selected student has passed the ELM,the probability the student is from out-of-state is_____ .

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. -Referring to Scenario 4-11,if an adult is selected at random,what is the probability that he/she is a registered voter who does not prefer to get his/her current information from the internet?

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 annual household income is over $50,000 if the residents of a household do not own 2 cars 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,if a randomly selected student is not from out-of-state,the probability the student has passed the ELM 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,what is the probability that a randomly selected student is a junior who does not live in a dormitory?

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?

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 took the bus?