Multiplication Rule of Probability
Multiplication Rule of Probability, when applied in the context of conditional probability, helps us calculate the probability of the intersection of two events when the probability of one event depends on the occurrence of the other event. This rule is crucial in understanding the joint probability of events under specific conditions.
In the context of conditional probability, the Multiplication Rule is often stated as follows:
P(A∩B) = P(A) × P(B∣A)
Here’s what each term represents:
- P(A∩B): This denotes the probability that both events A and B occur simultaneously.
- P(A): This represents the probability of event A happening.
- P(B∣A): This is the conditional probability of event B occurring given that event A has already occurred.
How to Apply the Multiplication Rule?
To apply the Multiplication Rule in the context of conditional probability, we can use the following steps:
- First we calculate the probability of event A occurring.
- Then, we compute the probability of event B occurring given that event A has occurred.
- Multiplying these probabilities together gives us the joint probability of both events happening under the specified conditions.
- This rule is particularly useful when dealing with events that are not independent, meaning that the occurrence of one event affects the probability of the other event.
Conditional Probability
Conditional probability is one type of probability in which the possibility of an event depends upon the existence of a previous event. As this type of event is very common in real life, conditional probability is often used to determine the probability of such cases.
Conditional probability describes the likelihood of an event (A) happening given that another event (B) has already occurred. In probability notation, this is denoted as A given B, expressed as P(A|B), indicating that the probability of event A is dependent on the occurrence of event B.
To know about conditional probability, we need to be familiar with independent events and dependent events. Let’s understand conditional probability, and its formula with solved examples in this article.
Conditional Probability
Table of Content
- What is Conditional Probability?
- Conditional Probability Definition
- Conditional Probability Formula
- How to Calculate Conditional Probability?
- Conditional Probability of Independent Events
- Conditional Probability vs Joint Probability vs Marginal Probability
- Conditional Probability and Bayes’ Theorem
- Conditional Probability Examples
- Tossing a Coin
- Drawing Cards
- Properties of Conditional Probability
- Multiplication Rule of Probability
- How to Apply the Multiplication Rule?
- Applications of Conditional Probability
- Conditional Probability Questions