Exam 4: Basic Probability

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

There are 47 contestants at a national dog show. How many different ways can contestants fill the first place, second place, and third place positions?

If P(A or B)= 1.0, then A and B must be collectively exhaustive.

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

TABLE 4-3 A survey is taken among customers of a fast-food restaurant to determine their 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 ________.

TABLE 4-3 A survey is taken among customers of a fast-food restaurant to determine their 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 is ________.

When A and B are mutually exclusive, P(A or B) can be found by adding P(A) and P(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: -Referring to Table 4-1, given that alcohol was not involved, what proportion of the accidents were multiple vehicle?

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

A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%), Disappointing (20%), and Highly Disappointing (?). If these are the only outcomes possible for the business venture, what is the chance that the business venture will be considered Highly Disappointing?

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 soda 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 is the probability that a randomly selected student is a junior who does not live in a dormitory?

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 only one of the twin brothers?

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 the cost is kept within budget and the campaign will increase sales is ________.

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

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 offers stock options to their board members?

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 has passed the ELM is ________.

An investment consultant is recommending a certain class of mutual funds to clients based on its exceptionally high probability of gain. It is an unethical practice not to also recommend a class of mutual funds with an exceptionally high probability of loss.

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?

Four freshmen are to be assigned to eleven empty rooms in a student dormitory. 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 freshmen be assigned?