Exam 4: Basic Probability

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

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 4-6 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 .

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"?

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 both house sales and 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 neither the cost is kept within budget nor the campaign will increase sales is:

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 and prefers chicken is .

If the outcome of event A is not affected by event B, then events A and B are said to be

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%?

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?

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?

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 and did not offer stock options to their board members?

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 not kept within budget or the campaign will not increase sales 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 .

The collection of all the possible events is called a sample space.

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?

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 4-3 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 a child and prefers chicken is .

A high school debate team of 4 is to be chosen from a class of 35.How many possible ways can the team be formed?

If event A and event B cannot occur at the same time, then events A and B are said to be