Events A and B are independent if: **knowing whether A occured does not change the probability of B**. Mathematically, can say in two equivalent ways: P(B|A) = P(B) P(A and B) = P(B ∩ A) = P(B) × P(A).

## Are events A and B independent example?

**Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true**. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.

## How do you know if events A and B are independent or dependent?

To test whether two events A and B are independent, calculate P(A), P(B), and P(A ∩ B), and then check whether P(A ∩ B) equals P(A)P(B). If they are equal, A and B are independent; if not, they are dependent.

## Are A and B dependent events?

A and B are said to be **Independent events**, if the probability of occurrence of an event A is not affected by the occurrence of another event B.

## Are A and B complement independent events?

This argument shows that if two events are independent, then each event is independent of the complement of the other. Therefore **A’ and B’ are also independent events**.

## Are A and B mutually exclusive?

Therefore, A and B are **not mutually exclusive**.

## Are two events independent?

In probability, we say **two events are independent if knowing one event occurred doesn’t change the probability of the other event**. For example, the probability that a fair coin shows “heads” after being flipped is 1 / 2 1/2 1/2 .

## How do you know if two variables are independent?

You can tell if two random variables are independent **by looking at their individual probabilities**. If those probabilities don’t change when the events meet, then those variables are independent. Another way of saying this is that if the two variables are correlated, then they are not independent.

## What is an example of an independent event?

Independent events are those events whose occurrence is not dependent on any other event. For example, **if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail**. In both cases, the occurrence of both events is independent of each other.

## When events A and B are said to be independent What does that mean?

Events A and B are independent if: **knowing whether A occured does not change the probability of B**. Mathematically, can say in two equivalent ways: P(B|A) = P(B) P(A and B) = P(B ∩ A) = P(B) × P(A).

## What are independent dependent events?

Dependent events influence the probability of other events – or their probability of occurring is affected by other events. Independent events do not affect one another and do not increase or decrease the probability of another event happening.

## What are independent events in probability?

Two events are independent **if the occurrence of one event does not affect the chances of the occurrence of the other event**. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)

## Are mutually exclusive events independent?

If two events are mutually exclusive then they do not occur simultaneously, hence they are **not independent**.

## Are A and B independent if A and B are independent?

**If A and B are independent events, then the events A and B’ are also independent**.

## For which of the following probability assignments are events A and BB independent?

Two events A and B are said to be independent if and only if P(A / B) = P(B) or P(B / A) = P(A). If **P(A) > 0, P(B) > 0, and P(A nB) = 0**, then the events A and B are independent.

## Is the complement set independent?

In conclusion, **if two events are independent, then their complements are also independent**.

### References:

- https://www.statisticshowto.com/probability-and-statistics/dependent-events-independent/
- https://www.zweigmedia.com/RealWorld/tutorialsf15e/frames7_5C.html
- https://byjus.com/jee/dependent-events-in-probability/
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- https://opentextbc.ca/introstatopenstax/chapter/independent-and-mutually-exclusive-events/
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