Exam 4: Basic Probability

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 4-8 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 independent.

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closing price. Based on the closing price of the stock collected over the last month, 25% of the days the closing price was higher than previous day's closing price, 45% was lower than previous day's and 30% was the same as previous day's. Based on this information, the probability that tomorrow's closing price will be higher than today's is 25%. This is an example of using which of the following probability approach?

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, if a randomly selected student lives in the dormitory, what is the probability that the student is a freshman?

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

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 independent of whether stock options are offered to their board members and why?

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

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

TABLE 4-11 A sample of 300 adults is selected. The contingency table below shows their registration status and their preferred source of information on current events. Preferred source of information Voting registration status Television Newspapers Radio Internet Registered 45 30 45 36 Not registered 35 44 45 20 -Referring to Table 4-11, if an adult is selected at random, what is the probability that he/she is a not a registered voter or does not prefer to get his/her current information from the Internet?

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 that a person prefers hamburger. The probability that this individual is a child 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?

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 ________.

An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women and 7 men. How many different ways can this team of 5 be formed?

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? 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?

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

TABLE 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 Table 4-12, if Jake, in fact, gets to the test on time, what is the probability that he took the bus?

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. The events increase in house sales and no increase in house sales in the next 6 months are

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 two events "preferring water" and "being a male" are independent.

When using the general multiplication rule, P(A and B)is equal to

If two events are mutually exclusive, what is the probability that one or the other occurs?