Let A and B be events such that P(A∩B) = 1/4, P( ˜ A) = 1/3, and P(B) = 1/2. What is P(A∪B)
If events are independent
\[P(A \cap B) = P(A)*P(B)\]
\[P(A \cap B) = 1/4\]
\[P(\overline{A})=1/3\]
probability_a_complement=1/3
probability_a= 1- probability_a_complement
probability_b= 1/2
probability_a_and_b = probability_a * probability_b
probability_a_and_b## [1] 0.3333333\[P(A \cap B) \neq P(A)*P(B)\]
Based on this, the events are not mutualy exclusive and dependent. In this case:
\[P(A \cup B) = P(A)+P(B)-P(A \cap B)\]
probability_a_or_b = probability_a + probability_b - probability_a_and_b
probability_a_or_b## [1] 0.8333333The answer is 0.83