Understanding Independent Events in Probability Theory | Explained with Examples

compound events whose outcomes do not affect each other

Compound events whose outcomes do not affect each other are referred to as independent events

Compound events whose outcomes do not affect each other are referred to as independent events.

In probability theory, two events are considered independent if the occurrence or outcome of one event does not affect the occurrence or outcome of the other event. This means that the probability of one event happening is not influenced by the occurrence or non-occurrence of the other event.

Mathematically, if A and B are two independent events, then the probability of both events occurring is equal to the product of their individual probabilities. This is represented by the formula:

P(A and B) = P(A) * P(B)

For example, let’s say you are rolling two fair six-sided dice. The probability of getting a 4 on the first die is 1/6, and the probability of getting a 3 on the second die is also 1/6. Since these events are independent and the outcome of one die does not influence the other, the probability of getting a 4 on the first die and a 3 on the second die is calculated as:

P(4 on first die and 3 on second die) = P(4 on first die) * P(3 on second die) = (1/6) * (1/6) = 1/36

Note that this equation holds true only if the events are truly independent, meaning there is no relationship or connection between them.

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