Exam 4: Basic Probability

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 4-11 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 who does not prefer to get his/her current information from the internet?

Eleven freshmen are to be assigned to eleven empty rooms in a student dormitory.Each roomis considered unique so that it matters who is being assigned to which room.How many different ways can those eleven freshmen be allocated?

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

Simple probability is also called

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?

SCENARIO 4-3 A survey is taken among customers of a fast-food restaurant to determine 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 Scenario 4-3, the probability that a randomly selected individual is an adult, or a child is .

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

If $\mathrm { P } ( A \text { and } B ) = 0$ , then A and B must be mutually exclusive.

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 prefers soda.Then the probability the patron is a male is .

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 unethical practice not toalso recommend a class of mutual funds with an exceptionally high probability of loss.

If two equally likely events A and B are collectively exhaustive, what is the probability that eventA occurs?

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, what is the probability that an adult who prefers to get his/her current information from the internet will be a registered voter?

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:

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 4-11 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 or prefers to get his/her current information from radio?

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 "being a male" are independent.

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

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 southern Texas, the probability the student has not passed the ELM is .

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 not include any of the twin brothers?