Union and Intersection in Probability

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Union and intersection are two concepts in the probability that describe the relationship between different events. Union and intersection can be useful for calculating probabilities when multiple events are involved.

Union:

The union of two events is the set of all outcomes that belong to either event. For example, if event A is the set of all outcomes that result in a number less than 5 (1, 2, 3 or 4) when rolling a die, and event B is the set of all outcomes that result in an even number (2, 4, or 6) when rolling a die. The union of events A and B would be the set of all outcomes that result in a number less than 5 OR an even number when rolling a die.

In that case, you could use the union of events A and B to find the total number of outcomes that would be considered successful. In this case, the resulting numbers will be (1, 2, 3, 4, 6). Each of these numbers meets the first OR the second requirement.

Intersection:

The intersection of two events is the set of all outcomes that belong to both events. For example, if event A is the set of all outcomes that result in a number less than 5 (1, 2, 3 or 4) when rolling a die, and event B is the set of all outcomes that result in an even number (2, 4, or 6) when rolling a die. The intersection of events A and B would be the set of all outcomes that result in a number less than 5 AND an even number when rolling a die. 

In that case, you could use the intersection of events A and B to find the total number of outcomes that would be considered successful. In this case, the resulting numbers will be (2, 4). Each of these numbers meets the first AND the second requirement.

Finally, you could divide the number of successful outcomes by the total number of possible outcomes to calculate the probability.


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