Understanding Dependent Events | Probability and Calculation

Dependent Events

Dependent events refer to a situation in probability where the outcome of one event affects the outcome of another event

Dependent events refer to a situation in probability where the outcome of one event affects the outcome of another event. In other words, the occurrence or non-occurrence of one event changes the probability of the occurrence of another event.

To understand dependent events, let’s consider an example. Suppose we have two events: Event A and Event B. If the occurrence of Event A increases the likelihood of Event B occurring, we say that Event B is dependent on Event A.

For example, let’s say we draw two cards from a deck without replacement. The first event is drawing a red card, and the second event is drawing a black card. The first card we draw is a red card, so the probability of drawing a black card for the second event decreases because there are now fewer black cards in the deck. Therefore, the second event (drawing a black card) is dependent on the outcome of the first event (drawing a red card).

To calculate the probability of dependent events, we need to consider the outcome of each event separately. We multiply the probability of the first event by the conditional probability of the second event, given that the first event has already occurred.

In our example, let’s assume the probability of drawing a red card is 1/2. After drawing a red card, the probability of drawing a black card is now 26/51 (since there are 26 black cards left out of the remaining 51 cards). So, the probability of both events occurring (drawing a red card and then drawing a black card) is (1/2) * (26/51) = 13/51.

In summary, dependent events occur when the outcome of one event affects the probability of another event. To calculate the probability of dependent events, we need to consider the probabilities of each event separately, taking into account the outcome of the previous event.

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