Chap 5 quiz
A coin is tossed four times. The joint probability that all four tosses will result in a head is ¼ or 0.25.
False Each outcome's probability is 0.5. The joint probability is (0.5)(0.5)(0.5)(0.5) = 0.0625.
The joint probability of two independent events, A and B, is computed as P(A and B) = P(A) × P(B).
True For two independent events (A and B), the probability that A and B will both occur is found by multiplying the two probabilities. This is the special rule of multiplication.
For a selected group of objects, there are as many combinations as there are different ways in which to order those objects.
False Order of objects is not important for combinations. The same set of objects in any order is just one combination. This is in contrast to permutations, where each different ordering of the same objects is a separate permutation.
The probability of rolling a 3 or 2 on a single die is an example of conditional probability.
False This is an example of classical probability. Classical probability is based on the assumption that the outcomes of an experiment (e.g. rolling a die) are equally likely. Conditional probability is the probability of a particular event occurring, given that another event has occurred (covered under LO5-4).
If two events are mutually exclusive, then P(A and B) = P(A) × P(B).
False If two events are mutually exclusive, the joint probability P(A and B) = 0.
A joint probability measures the likelihood that two or more events will happen concurrently.
True A joint probability measures the chance that two or more events can happen at the same time. If the events are mutually exclusive, the joint probability is zero.
The complement rule states that the probability of an event occurring is equal to one minus the probability of it not occurring.
True Complement rule P(A) = 1 − P(~A), If P(A) and P(~A) are complements, then P(A) = 1 − P(~A) and P(~A) = 1 − P(A).
The joint probability of two events, A and B, that are NOT independent is computed as P(A and B) = P(A) × P(B|A).
True General rule of multiplication P(A and B) = P(A)P(B|A).For two events, A and B, that are not independent, the conditional probability is represented as P(B|A), and expressed as the probability of B given A.
If there are "m" ways of doing one thing, and "n" ways of doing another thing, there are (m) × (n) ways of doing both. The multiplication formula solves for the total number of arrangements by multiplying (m) × (n).
True The multiplication formula solves for the total number of arrangements by multiplying. It can be used for two (or more) events. For example, if there are three events m, n, and o, the total number of arrangements = (m)(n)(o).
To apply the special rule of addition, the events must be mutually exclusive.
True The special rule of addition requires that events be mutually exclusive. As illustrated using a Venn diagram, this occurs when there is no intersection or overlap of events. Since the events cannot occur concurrently, the joint probability is zero.
The probability of rolling a 3 or 2 on a single roll of a die is an example of mutually exclusive events.
True This is mutually exclusive as you cannot roll both 2 and 3 at the same time. Only one of these events can happen on a single roll of a die.
An individual can assign a subjective probability to an event based on whatever information is available.
True When an individual evaluates the available opinions and information and then estimates or assigns the probability. This probability is called subjective probability.
