Exam 4: Basic Probability

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 improperly sealed is ________.

The collection of all the possible events is called a sample space.

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, suppose a randomly selected patron prefers soda. Then the probability the patron is a male 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, is "the size of the company" independent of "whether stock options are offered to their board members" and why?

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

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

If P(A)= 0.4 and P(B)= 0.6, then A and B must be mutually exclusive.

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 and prefers chicken is ________.

TABLE 4-12 Jake wakes 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 rode his bike?

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. -Referring to Table 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter or prefers to get his/her current information from radio?

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