# A and B Are Two Independent Events

A and B Are Two Independent Events

We often hear people say things like “A and B are two independent events.” What does this mean?

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## Introduction

A and B are two events that are said to be independent if the occurrence of event A does not affect the probability of event B occurring and vice versa. In other words, the events are not related in any way and the probability of one event occurring is not affected by whether the other event occurs.

### What is the probability of two events?

When we say that two events are independent, we mean that the probability of one event does not affect the probability of the other event. In other words, the two events are not related. For example, when you flip a coin, the probability of getting heads is ½. The probability of getting tails is also ½. The probability of getting heads does not affect the probability of getting tails and vice versa. This is why we say that flipping a coin is an example of two independent events.

But what happens when we have two events that are not independent? This is where things start to get more complicated. Let’s say we have a bag with two pieces of candy in it: a red piece and a green piece. If we reach into the bag and randomly select one piece of candy, what is the probability that it will be green?

In this case, the answer is 1/2 or 50%. But what if we already know that the first piece of candy selected from the bag was red? What is the probability that the second piece of candy will be green?

In this case, the answer is 1 or 100%. Why is this? Because if the first piece of candy was red, then we know that there is only one other piece of candy in the bag (the green piece). Therefore, the probability of selecting it is 1 or 100%.

### What is an independent event?

An independent event is an event that is not affected by any other events. In other words, the outcome of one event does not affect the outcome of another event. For example, if you roll a die and then flip a coin, the result of the die roll does not affect the result of the coin flip. These are two independent events.

## A and B Are Two Independent Events

A and B are said to be independent events if the occurrence of event A does not affect the probability of event B occurring and vice versa. In other words, the events are not dependent on each other in any way.

## What is the probability of A and B?

The probability of A and B is the probability of A times the probability of B. This is because A and B are two independent events.

## What is the probability of A and not B?

There are three possible outcomes when two events, A and B, are taking place: A and B both happen, A happens and B does not, or B happens and A does not. If we know the probability of each of these events occurring, then we can calculate the probability of A and not B happening.

The probability of A and not B happening is equal to the probability of A happening multiplied by the probability of B not happening. In other words, P(A∩¬B)=P(A)×P(¬B).

For example, let’s say that the probability of event A is 0.2 (or 20%) and the probability of event B is 0.5 (or 50%). The probability that both A and B happen would be 0.2 x 0.5 = 0.1 (or 10%). The probability that only event A happens would be 0.2 x (1 – 0.5) = 0.1 (or 10%). And finally, the probability that only event B happens would be (1 – 0.2) x 0.5 = 0.4 (or 40%). Therefore, the probability of A and not B happening is equal to 10% + 40% = 50%.

## Conclusion

In conclusion, we have shown that A and B are two independent events. This means that the probability of A occurring is not affected by whether or not B occurs, and vice versa. This is an important result to remember when performing statistical analysis, as it can help simplify calculations.

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