let A B and C are three arbitrary event . find the probability both a and b but not c occur
To find the probability that both A and B occur but not C, we can use the principle of inclusion-exclusion.
Let P(A) be the probability of event A occurring.
Let P(B) be the probability of event B occurring.
Let P(C) be the probability of event C occurring.
The probability of both A and B occurring is given by P(A and B).
The probability of not C occurring is given by 1 - P(C).
The probability of both A and B occurring but not C is:
P(A and B and not C) = P(A) * P(B) * (1 - P(C))
Note that this assumes that events A, B, and C are independent. If they are dependent, the calculation may require additional information.