Two events are independent if the occurrence of one event provides no information about the probability of the other event occurring. Mathematically, this is expressed as P(A|B) = P(A), meaning the conditional probability of A given B is simply the probability of A.
432
Under what condition are two events defined as being equally likely?
Two events are considered equally likely if the probability of occurrence for each event is identical. This means that in a given experiment, there is no statistical bias favoring one outcome over the other, resulting in an equal chance for each event to occur within the defined sample space.
433
What term describes events that share one or more common sample points?
In probability theory, two events are considered overlapping or non-mutually exclusive if they share at least one common outcome in the sample space. This means the intersection of the two events is not an empty set, allowing both events to occur simultaneously.
434
What is the term for a counting method that determines the number of possible outcomes without requiring an exhaustive list?
Combinatorial methods, often applied to multiple experiments or complex events, allow for the calculation of the total number of outcomes using mathematical principles like permutations and combinations, rather than manual enumeration.
435
What term describes a process or measurement where the outcome is determined by chance?
A random experiment is a process or procedure that can be repeated under identical conditions, where the outcome cannot be predicted with certainty in advance, but the set of all possible outcomes is known.
436
If an experiment involves selecting 2 items from a set of 4 distinct items, what is the total number of possible permutations?
The number of permutations of n items taken r at a time is given by P(n, r) = n! / (n-r)!. For n=4 and r=2, the calculation is 4! / (4-2)! = 24 / 2 = 12. There is a conflict as the source answer is 24, which would be 4! (permutations of all items). We preserve the source key.
437
What term describes an event that consists of exactly one sample point from the sample space?
In probability theory, an elementary event (also known as a simple event or sample point) is an event that contains exactly one outcome in the sample space. It is the most basic building block of a probability space.
438
In probability theory, what does a value of zero represent when measuring the likelihood of an event?
The probability of an event is a number between 0 and 1 inclusive. A probability of 0 indicates that the event is impossible, meaning it cannot occur under the given conditions. Conversely, a probability of 1 indicates that the event is certain to occur.
439
What term describes a set of events that, when combined, cover the entire sample space?
Events are considered collectively exhaustive if their union comprises the entire sample space. This means that at least one of the events must occur. While the provided answer key suggests 'Equally', in formal statistical terminology, this concept is defined as 'Exhaustive events'.
440
What is the mathematical expression for the joint probability of two independent events, J and K?
Two events are considered independent if the occurrence of one does not affect the probability of the occurrence of the other. For independent events J and K, the joint probability, denoted as P(J and K) or P(J ∩ K), is calculated by multiplying their individual probabilities: P(J) multiplied by P(K).
