suresh In probability theory, the difference between independent and dependent events lies in the relationship between the occurrence of one event and the occurrence of another.
Independent events are events that do not affect each other, meaning the outcome of one event does not impact the outcome of the other. Mathematically, if events A and B are independent, then the probability of both events happening is the product of the probabilities of each event occurring independently.
Example of independent events:
- Rolling a dice and flipping a coin are independent events since the outcome of one does not affect the outcome of the other.
On the other hand, dependent events are events where the outcome of one event is influenced by the outcome of another event. Mathematically, if events A and B are dependent, then the probability of both events happening is the probability of event A multiplied by the conditional probability of event B given that event A has already occurred.
Example of dependent events:
- Drawing two cards from a deck without replacement is an example of dependent events, as the likelihood of drawing the second card is influenced by what was drawn first.
Understanding the distinction between independent and dependent events is crucial in calculating the probabilities of different scenarios in probability theory.
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