Exam 4: Basic Probability

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

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

According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents of a household do not own two cars and have an income over $50,000 a year is ________.

If P(A and B)= 0, then A and B must be mutually exclusive.

If either A or B must occur the events are called mutually exclusive.

TABLE 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 Table 4-4, the probability a randomly selected patron is a female who prefers water is ________.

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, what percentage of the students do not live in a dormitory?

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 not from southern Texas and 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. Assuming that the two events are independent, the probability that neither the cost is kept within budget nor the campaign will increase sales is ________.

A new model car from Ford Motor Company offers a keyless entry system that utilizes a four-letter code. How many different possible combinations are there for the code?

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: -Referring to Table 4-1, given alcohol was involved, what proportion of accidents involved a single vehicle?

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, what is the probability that a randomly selected student is a sophomore who does not live in a dormitory?

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closing price. 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?

TABLE 4-7 The next state lottery will have the following -Referring to Table 4-7, the probability that you win any money is ________.

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

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

There are only four empty rooms available in a student dormitory for eleven new freshmen. All the rooms are considered as homogenous so that it does not matter who is being assigned to which room. How many different ways can those four empty rooms be filled with one student per room?

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"?

TABLE 4-5 In a meat packaging plant Machine A accounts for 60% of the plant's output, while Machine B accounts for 40% of the plant's output. In total, 4% of the packages are improperly sealed. Also, 3% of the packages are from Machine A and are improperly sealed. -Referring to Table 4-5, if a package selected at random came from Machine B, the probability that it is properly sealed is ________.

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 noncash 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 does not offer stock options to their board members?