58.9k views
1 vote
If A, B, and C are mutually exclusive, find P(A ∪ B ∪ C)?

1 Answer

2 votes

Final answer:

To find the probability of mutually exclusive events A, B, or C occurring, we add the individual probabilities of each event, since there is no overlap between them.

Step-by-step explanation:

When events A, B, and C are mutually exclusive, it means they cannot occur at the same time. Therefore, the probability of A and B, A and C, or B and C occurring at the same time is zero. To find the probability of A, B, or C occurring, denoted as P(A ∪ B ∪ C), we simply add the probabilities of each event happening independently, since there is no overlap between them.

Thus, the formula to find the union of three mutually exclusive events is:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C)

This formula applies because there is no need to subtract any intersecting probabilities, as there are none for mutually exclusive events.

User Skhurams
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.