Question

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

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Murray

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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%.

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