Exam 4: Basic Probability

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

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. What is the probability that house sales will increase but interest rates will not during the next 6 months?

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, assume we know the person is a child. The probability that this individual prefers hamburger is ______.

If P(A and B) = 0, then A and B must be collectively exhaustive.

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, 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?

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 play a 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 alcohol was not involved, what proportion of the accidents were multiple vehicle?

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. Assuming that the two events are independent, what is the probability that the cost is kept within budget and the campaign will increase sales?

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

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

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 play a 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, what proportion of accidents involved more than one vehicle?

Selection of raffle tickets from a large bowl is an example of

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

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

$\text { TABLE 4-2 }$ 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 Studyingror Exam 80 20 Went Bar Hopping 30 70 -Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm and also went bar hopping the weekend before the midterm?

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

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, what proportion of accidents involved alcohol and a single vehicle?

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closed. Without any prior information that may affect the price of the stock tomorrow, the probability that it will close higher than today's close is 1/3. This is an example of using which of the following probability approach?

$\text { TABLE 4-6 }$ 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 Table 4-6, if a randomly selected student has not passed the ELM, the probability the student is from southern Texas is_____ .

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

$\text { TABLE 4-6 }$ 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 Table 4-6, the probability that a randomly selected student is someone from northern Texas who has not passed the ELM is ____.