Understanding Dependent Events in Probability | Definition and Examples

Dependent events

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

Dependent events in probability refer to a situation where the outcome or occurrence of one event affects the outcome or occurrence of another event. In other words, the probability of the second event happening depends on whether or not the first event has already occurred.

To better understand dependent events, let’s consider an example. Suppose you have a bag containing 5 red balls and 3 blue balls. If you randomly select a ball from the bag without replacement, the events of selecting the first ball and then the second ball are dependent.

In this scenario, the probability of selecting a red ball on the first draw is 5/8 since there are 5 red balls out of the total 8 balls. However, if you indeed select a red ball on the first draw, the probability of selecting a red ball on the second draw changes. After removing one red ball from the bag, there are 4 red balls and 7 balls remaining. Thus, the probability of selecting a red ball on the second draw becomes 4/7.

This example demonstrates that the outcome of the first event (selecting a red ball) affects the outcome of the second event (selecting another red ball) because the sample space or available choices for the second event changes based on the first event.

In summary, dependent events occur when the outcome of one event influences the probability or outcome of another event. These events are often encountered in probability experiments where outcomes are not replaced before the next event takes place.

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