5.- From the probabilities: 𝐏(𝐁) = 𝟑𝟎% 𝐏(𝐀 ∩ 𝐁) = 𝟐𝟎% 𝐏(𝐀 ̅) = 𝟕𝟎% You are asked to calculate: 𝐏(𝐀 ∪ 𝐁)

To calculate the probability of the union of events A and B, you can use the probability addition rule: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Given the probabilities:\[ P(B) = 30\% \]\[ P(A \cap B) = 20\% \] You are asked to calculate \( P(A \cup B) \). First, let's find P(A) using the complement rule:\[ P(\overline{A}) = 70\% \] The complement rule states that \( P(\overline{A}) = 1 - P(A) \),\: so\[ P(A) = 1 - P(\overline{A}) \]\[ P(A) = 1 - 0.70 = 0.30 \] Now, substitute these values into the probability addition rule:\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]\[ P(A \cup B) = 0.30 + 0.30 - 0.20 \]\[ P(A \cup B) = 0.40 \] So, the probability of the union of events A and B, \( P(A \cup B) \), is 40%.