If I am using a venn diagram, the probability that event A occurs or event B occurs but not both. What is my formula? I am soooo very confused..
Need data.
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To find the probability that event A occurs or event B occurs but not both, you can use the principle of inclusion-exclusion. This principle states that the probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection.
Let's denote the following probabilities:
- P(A) represents the probability of event A occurring,
- P(B) represents the probability of event B occurring,
- P(A ∩ B) represents the probability of both events A and B occurring.
The probability that event A occurs or event B occurs but not both can be calculated using the formula:
P(A or B, but not both) = P(A) + P(B) - 2P(A ∩ B)
Explanation:
1. P(A) represents the probability of event A occurring.
2. P(B) represents the probability of event B occurring.
3. P(A ∩ B) represents the probability of both events A and B occurring, which is the intersection of the two events.
4. P(A) + P(B) represents the sum of the probabilities of events A and B occurring, which includes the probability of their intersection twice (once in P(A) and once in P(B)).
5. To avoid double counting the probability of the intersection, we subtract twice the probability of their intersection, which is why we subtract 2P(A ∩ B).
By plugging in the values for P(A), P(B), and P(A ∩ B), you can calculate the probability of event A occurring or event B occurring but not both, using the formula mentioned above.