What are dependent events in probability?

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Dependent events in probability are events where the occurrence or non-occurrence of one event affects the probability of the occurrence of another event. In other words, the probability of one event is not independent of the other event. This means that the probability of one event changes based on the occurrence or non-occurrence of the other event.

For example, consider rolling two dice. The probability of rolling a 6 on the first die is 1/6. However, if the first die shows a 6, the probability of rolling a 6 on the second die is 1/6, but if the first die shows a number other than 6, the probability of rolling a 6 on the second die is 1/6. In this case, the occurrence of one event (rolling a 6 on the first die) affects the probability of the other event (rolling a 6 on the second die).

Dependent events are often denoted as $$A$$ and $$B$$, where $$A$$ is the first event and $$B$$ is the second event. The probability of event $$B$$ occurring given that event $$A$$ has occurred is denoted as $$P(B|A)$$. This is different from the probability of event $$B$$ occurring independently of event $$A$$, which is denoted as $$P(B)$$.
Dependent events in probability are events where the occurrence of one affects the probability of the other. For example, rolling two dice, the outcome of the first die influences the probability of the second die's outcome.

What are dependent events in probability?

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