# Probability Question - Prove Formula

• GreenPrint
In summary, the formula for calculating probability is P(E) = Number of favorable outcomes / Total number of outcomes. It can be proved using mathematical principles such as the law of total probability, Bayes' theorem, and the rules of probability. Understanding probability is important in various fields and can help us make informed decisions and predictions. Common misconceptions about probability include the belief that past events can influence future outcomes and that probability always results in whole numbers. Probability can be applied in real-life situations such as weather forecasting, risk assessment, decision making, and analyzing market trends in business.
GreenPrint

## Homework Statement

Hi,

Prove P(AUB|C) = P(A|C)+P(B|C)-P(A∩B|C)

## The Attempt at a Solution

I start off from here

$P(AUB|C)=\frac{P(AUB)P(C|AUB)}{P(C)}$

I don't know where to go from here. Thanks for any help that you can provide.

I think I actually figured this one. I realize that A, B, C may not necessairly be independent and for whatever reason I thought they where so I wasn't getting the correct answer

## What is the formula for calculating probability?

The formula for calculating probability is: P(E) = Number of favorable outcomes / Total number of outcomes

## How do you prove the probability formula?

The probability formula can be proved using mathematical principles such as the law of total probability, Bayes' theorem, and the rules of probability. These principles provide a logical and mathematical explanation for the formula.

## What is the importance of understanding probability?

Understanding probability is crucial in many fields such as science, business, and statistics. It allows us to make informed decisions and predictions based on data and can help us understand the likelihood of certain events occurring.

## What are the common misconceptions about probability?

One common misconception about probability is that past events can influence future outcomes. In reality, each event is independent and has its own probability. Another misconception is that probability always results in a whole number, when in fact, it can also result in fractions or decimals.

## How can probability be applied in real life?

Probability is used in many real-life situations, such as weather forecasting, risk assessment, and decision making. It can also be applied in games of chance, like rolling a dice or flipping a coin. In business, probability can be used to analyze market trends and make predictions about future sales.

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