Question
5.- From the probabilities: π(π) = ππ% π(π β© π) = ππ% π(π Μ ) = ππ% You are asked to calculate: π(π βͺ π)
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Answer to a math question 5.- From the probabilities: π(π) = ππ% π(π β© π) = ππ% π(π Μ ) = ππ% You are asked to calculate: π(π βͺ π)
Murray
4.592 Answers
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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