event

Examples of event in the following topics:

• Complementary Events

  • The complement of $A$ is the event in which $A$ does not occur.
  • In probability theory, the complement of any event $A$ is the event $[\text{not}\ A]$, i.e. the event in which $A$ does not occur.
  • Generally, there is only one event $B$ such that $A$ and $B$ are both mutually exclusive and exhaustive; that event is the complement of $A$ .
  • The complement of an event $A$ is usually denoted as $A'$, $A^c$ or $\bar{A}$.
  • Finally, let's examine a non-example of complementary events.

• Independent Events

  • Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs.
  • For example, the outcomes of two roles of a fair die are independent events.
  • To show two events are independent, you must show only one of the above conditions.
  • If two events are NOT independent, then we say that they are dependent.
  • The events are considered to be dependent or not independent.

• Fundamentals of Probability

  • An impossible event, or an event that never occurs, has a probability of $0$.
  • An event that always occurs has a probability of $1$.
  • The probability that an event does not occur is $1$ minus the probability that the event does occur.
  • These events are called complementary events, and this rule is sometimes called the complement rule.
  • Suppose $A$ is the event exactly one head occurs, and $B$ is the event exactly two tails occur.

• Conditional Probability

  • The conditional probability of an event is the probability that an event will occur given that another event has occurred.
  • Our estimation of the likelihood of an event can change if we know that some other event has occurred.
  • The conditional probability $\displaystyle P(B|A)$ of an event $B$, given an event $A$, is defined by:
  • Suppose that $B$ is the event that at least one heads occurs and $A$ is the event that all $3$ coins are the same.
  • If the knowledge that event $A$ occurs does not change the probability that event $B$ occurs, then $A$ and $B$ are independent events, and thus, $P(B|A) = P(B)$.

• Guidelines for Plotting Frequency Distributions

  • The frequency distribution of events is the number of times each event occurred in an experiment or study.
  • In statistics, the frequency (or absolute frequency) of an event is the number of times the event occurred in an experiment or study.
  • The relative frequency (or empirical probability) of an event refers to the absolute frequency normalized by the total number of events.
  • The values of all events can be plotted to produce a frequency distribution.

• Statistical Literacy

  • Critics have said that extreme events in reality are more frequent than would be expected assuming normality.
  • A recent article discussing how to protect investments against extreme events defined "tail risk" as "A tail risk, or extreme shock to financial markets, is technically defined as an investment that moves more than three standard deviations from the mean of a normal distribution of investment returns."
  • Tail risk can be evaluated by assuming a normal distribution and computing the probability of such an event.
  • Events more than three standard deviations from the mean are very rare for normal distributions.
  • If the normal distribution is used to assess the probability of tail events defined this way, then the "tail risk" will be underestimated.

• Independence

  • The concept of independence extends to dealing with collections of more than two events.
  • Two events are independent if any of the following are true:
  • For independent events, the condition does not change the probability for the event.
  • Consider a fair die role, which provides another example of independent events.
  • First, note that each coin flip is an independent event.

• Student Learning Outcomes

  • Determine whether two events are mutually exclusive and whether two events are independent.

• Disjoint or mutually exclusive outcomes

  • These sets are commonly called events.
  • (a) Verify the probability of event A, P(A), is 1=3 using the Addition Rule. ( b) Do the same for event B.
  • ( b) Are events B and D disjoint?
  • (c) Are events A and D disjoint?
  • Compute the probability that either event B or event D occurs.

• Mutually Exclusive Events

  • Let event A = a face is odd.
  • Let event B = a face is even.
  • Let event E = all faces less than 5.
  • Recall that the event C is { 3, 5 } and event A is { 1, 3, 5 } .
  • Let event G = taking a math class.