Addition Rule for Probabilities

The addition rule for probabilities is a fundamental rule in probability theory that states that the probability of two events occurring together is equal to the sum of the probabilities of each event occurring individually. This rule can be used to calculate the probability of any event, even if the events are not independent.

The addition rule for probabilities is often used to calculate the probability of a compound event, which is an event that is made up of two or more simpler events. For example, the probability of rolling a 6 on a die is 1/6, and the probability of rolling a 4 on a die is 1/6. The probability of rolling either a 6 or a 4 is 1/6 + 1/6 = 1/3.

The addition rule for probabilities can also be used to calculate the probability of an event that is not independent of another event. For example, the probability of getting a head on a coin toss is 1/2, and the probability of getting a tail on a coin toss is 1/2. The probability of getting either a head or a tail is 1/2 + 1/2 = 1.

The addition rule for probabilities is a powerful tool that can be used to calculate the probability of any event. It is important to understand the rule and how to apply it in order to make accurate probability calculations.

Here are some additional examples of how the addition rule for probabilities can be used:

* The probability of getting a red card in a game of poker is 1/4, and the probability of getting a black card is 1/2. The probability of getting either a red card or a black card is 1/4 + 1/2 = 3/4.
* The probability of getting a 6 on a die is 1/6, and the probability of getting a 7 on a die is 1/6. The probability of getting either a 6 or a 7 is 1/6 + 1/6 = 1/3.
* The probability of getting a head on a coin toss is 1/2, and the probability of getting a tail on a coin toss is 1/2. The probability of getting either a head or a tail is 1/2 + 1/2 = 1.

The addition rule for probabilities is a fundamental rule in probability theory that can be used to calculate the probability of any event. It is important to understand the rule and how to apply it in order to make accurate probability calculations.