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## About Multiplication Theorem of Probability

The multiplication theorem of probability states that the probability of two or more events occurring is the product of their individual probabilities.

## Proof of Multiplication Rule Probability

To prove the multiplication rule probability, we will use the following equation:

P(A and B) = P(A) x P(B)

We will start by assuming that A and B are independent events. This means that the occurrence of one event does not affect the probability of the other event occurring. We can then use the fact that the probability of two independent events both occurring is the product of their individual probabilities. This will give us the following equation:

P(A and B) = P(A) x P(B)

= (0.5) x (0.5)

= 0.25

## Multiplication Theorem in Probability

Multiplication theorem in Probability is a theorem that states that the probability of two independent events occurring together is the product of their individual probabilities.

## Multiplication Theorem of Probability Examples

Problem 1

In a jar there are 6 green balls and 8 blue balls. What is the probability of picking a blue ball?

The probability of picking a blue ball is 8/14.

## Multiplication Rule of Probability for Independent Events

The multiplication rule of probability states that the probability of two or more independent events occurring is the product of their individual probabilities.

## Multiplication Rule of Probability for Dependent Events

If two events are dependent, then the probability of both events happening together is the product of the probabilities of the two individual events.