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What is the definition of a compound event?

A compound event is an event that has more than one possible outcomes. We have already seen the simple events and other types of events. In a compound event, an experiment gives more than one possible outcomes. Let us begin with defining the compound events.

What is an example of a compound event?

A compound event is the combination of two or more simple events (with two or more outcomes). The probability of drawing a heart, replacing the card, then drawing a spade. In a compound event, the numerator (“number of times it can occur”) will be greater than 1.

What is the definition of compound event in probability?

A compound probability combines at least two simple events, also known as a compound event. The probability that a coin will show heads when you toss only one coin is a simple event.

How do you find a compound event?

In mathematical terms: P(C) = P(A) + P(B). An inclusive compound event is one in which there is overlap between the multiple events. The formula for determining the probability of an inclusive compound event is: P(C) = P(A) + P(B) – P(A and B).

What is the difference between a simple event and a compound event?

A simple event results in just one outcome. For instance, if we flip one coin, it will result in just one outcome. The coin could either land on heads, or it could land on tails. A compound event is an event containing more than one outcome.

What is simple or compound event?

A simple event is one that can only happen in one way – in other words, it has a single outcome. A compound event is more complex than a simple event, as it involves the probability of more than one outcome. Another way to view compound events is as a combination of two or more simple events.

What is an example of a simple event?

In probability terms, a simple event refers to an event with a single outcome, for example, getting “heads” with a single toss of a coin, or rolling a 4 on a die.

What is simple and compound event in probability?

Simple events are events where one experiment happens at a time and it will have a single outcome such as tossing a coin. Compound events are events where there is more than one possible outcome such as roll a five using a 6-sided die.

What is a compound dependent event?

Sometimes, when you have a series of compound events, the outcome of the first event does affect the outcomes of the subsequent events. These events are called dependent events since the outcome of the second (or third) event depends on the outcome of the first event.

Are compound events dependent?

Independent and Dependent Events Suppose you flip a coin and roll a die at the same time. These are compound events. When events depend upon each other, they are called dependent events. Suppose you randomly draw a card from a standard deck and then randomly draw a second card without replacing the first.

What does P match mean?

Probability matching

How do you read Bayes Theorem?

Formula for Bayes’ Theorem

  1. P(A|B) – the probability of event A occurring, given event B has occurred.
  2. P(B|A) – the probability of event B occurring, given event A has occurred.
  3. P(A) – the probability of event A.
  4. P(B) – the probability of event B.

Why Bayes classifier is optimal?

The bayes classifier is the theoretically optimal classifier for a given classification problem. For a given input pattern, the Bayes classifier outputs the label that is the most likely, and thus provides a prediction that is the less likely to be an error compared with the other choices of label.

How do you derive Bayes Theorem?

Bayes Theorem Derivation. Bayes Theorem can be derived for events and random variables separately using the definition of conditional probability and density. Here, the joint probability P(A ⋂ B) of both events A and B being true such that, P(B ⋂ A) = P(A ⋂ B)

What is Bayes theorem and when can it be used?

More generally, Bayes’s theorem is used in any calculation in which a “marginal” probability is calculated (e.g., p(+), the probability of testing positive in the example) from likelihoods (e.g., p(+|s) and p(+|h), the probability of testing positive given being sick or healthy) and prior probabilities (p(s) and p(h)): …

Where does the Bayes rule can be used?

Where does the bayes rule can be used? Explanation: Bayes rule can be used to answer the probabilistic queries conditioned on one piece of evidence.

What is the name of P A in Bayes theorem context?

marginal probability

Why do we use naive Bayes algorithm?

Naive Bayes is suitable for solving multi-class prediction problems. If its assumption of the independence of features holds true, it can perform better than other models and requires much less training data. Naive Bayes is better suited for categorical input variables than numerical variables.

What does Bayes optimal mean?

The Bayes Optimal Classifier is a probabilistic model that makes the most probable prediction for a new example. Bayes Optimal Classifier is a probabilistic model that finds the most probable prediction using the training data and space of hypotheses to make a prediction for a new data instance.

Is Bayes classifier unique?

(In general, the Bayes optimal classifier need not be unique, since there may be several classifiers that achieve the same minimal error.)

Is naive Bayes optimal?

Classification Performance of Naive Bayes In a given dataset, two attributes may depend on each other, but the dependence may distribute evenly in each class. Clearly, in this case, the conditional independence assumption is vio- lated, but naive Bayes is still the optimal classifier.

Why is naive Bayes computationally efficient?

This can be useful in situations where the dataset is small compared to the number of features, such as images or texts. The computational efficiency of Naive Bayes lies in the fact that the runtime complexity of Naive Bayes classifier is O(nK), where n is the number of features and K is the number of label classes.

Can naive Bayes be nonlinear?

In general the naive Bayes classifier is not linear, but if the likelihood factors p(xi∣c) are from exponential families, the naive Bayes classifier corresponds to a linear classifier in a particular feature space.

How do you use naive Bayes?

Naive Bayes classifier calculates the probability of an event in the following steps:

  1. Step 1: Calculate the prior probability for given class labels.
  2. Step 2: Find Likelihood probability with each attribute for each class.
  3. Step 3: Put these value in Bayes Formula and calculate posterior probability.

When should I use naive Bayes?

Pros:

  1. It is easy and fast to predict class of test data set.
  2. When assumption of independence holds, a Naive Bayes classifier performs better compare to other models like logistic regression and you need less training data.
  3. It perform well in case of categorical input variables compared to numerical variable(s).