what are independent and dependent events

what are independent and dependent events


Independent events are events that are not affected by prior events or outcomes. For example, rolling a dice and flipping a coin are independent events because the outcome of one event does not affect the outcome of the other.


Dependent events are events that are affected by prior events or outcomes. For example, drawing two cards from a deck of cards and the outcome of the first card will affect the outcome of the second card.


how to know if events are dependent of independent in probability prove by formula and numerical question.


To determine if two events are dependent or independent, you can calculate the probability of the two events occurring together. If the probability of the two events occurring together is equal to the product of the individual probabilities of the two events, then the two events are independent. For example, if the probability of event A occurring is 0.5 and the probability of event B occurring is 0.3, then the probability of both events occurring together is 0.15 (0.5 x 0.3). If this probability is equal to the probability of both events occurring together, then the two events are independent.


You can also determine if two events are dependent or independent by calculating the conditional probability. If the probability of event A occurring given that event B has already occurred is the same as the probability of event A occurring on its own, then the two events are independent. For example, if the probability of event A occurring is 0.5 and the probability of event B occurring is 0.3, then the probability of event A occurring given that event B has occurred is also 0.5. If this is the case, then the two events are independent.

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