Exam 4: Basic Probability

If P(A and B) = 1, then A and B must be mutually exclusive.

Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A andB) = 0.1. Then P(A|B)= ______.

$\text { TABLE 4-2 }$ 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 Poorlyon Midterm Studyingfor Exam 80 20 Went Bar Hopping 30 70 -Referring to Table 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

TABLE 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 Table 4-9, is the size of the company statistically independent of whether stock options are offered to their board members and why?

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 1.. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events of increase in house sales and increase in interest rates in the next 6 months are

TABLE 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 Table 4-3, the probability that a randomly selected individual is a child or prefers hamburger is____ .

All the events in the sample space that are not part of the specified event are called

If two events are collectively exhaustive, what is the probability that both occur at the same time?

TABLE 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 Table 4-1, given that 3 vehicles were involved, what proportion of accidents involved alcohol?

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

TABLE 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 Table 4-10, what is the probability that a randomly selected worker had not claimed bias?

TABLE 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 Table 4-8, determine whether the class status of a student and whether the student lives in a dormitory are statistically independent.

$\text { TABLE 4-1 }$ Mothers Against Drunk Driving is a very visible group whose main 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: $\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of Vehicles Involved }$ Did alcohol playa role? 1 2 3 Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Table 4-1, given alcohol was involved, what proportion of accidents involved a single vehicle?

$\text { TABLE 4-10 }$ 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 Table 4-10, if a randomly selected worker had not claimed bias, what is the probability that the worker is white?

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 1.. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events of increase in house sales and no increase in house sales in the next 6 months are

If A and B cannot occur at the same time they are called mutually exclusive.

$\text { TABLE 4-3 }$ 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 Table 4-3, the probability that a randomly selected individual is an adult or a child is_____ .

$\text { TABLE 4-7 }$ The next state lottery will have the following payoffs possible with their associated probabilities. Payoff Probability \ 2.00 0.0500 \ 25.00 0.0100 \ 100.00 0.0050 \ 500.00 0.0010 \ 5,000.00 0.0005 \ 10.000.00 0.0001 You buy a single ticket. -Referring to Table 4-7, the probability that you win any money is _____.

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that the residents do not own 2 cars if annual household income is not over $25,000?

TABLE 4-1 Mothers Against Drunk Driving is a very visible group whose main 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 playa role? 1 2 3 Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Table 4-1, given that multiple vehicles were involved, what proportion of accidents involved alcohol?