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What is the probability of union of two events?

The probability of the union of two events is the sum of their individual probabilities minus their intersection.

When dealing with two events A and B, the union of the two events is denoted by A ∪ B and represents the event that either A or B or both occur. The probability of the union of two events can be calculated using the following formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

where P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A ∩ B) represents the probability of both A and B occurring.

To understand why we subtract the probability of the intersection, consider the following example: suppose we want to find the probability of rolling either a 1 or a 2 on a fair six-sided die. The probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, but the probability of rolling both a 1 and a 2 is 0. Therefore, the probability of rolling either a 1 or a 2 is:

P(1 ∪ 2) = P(1) + P(2) - P(1 ∩ 2)
= 1/6 + 1/6 - 0
= 1/3

In general, the probability of the union of two events is always greater than or equal to the probability of either event occurring individually, since the intersection of the two events can only decrease the probability of their union.

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