Probability
Basic Probability
Grade 12
Question:
<p>The probability that at least one of the events A and B occurs is \(\frac{3}{5}\). If A and B occur simultaneously with probability \(\frac{1}{5}\), then \(P(A) + P(B)\) is</p>
<p>(a) \(\frac{2}{5}\)</p>
<p>(b) \(\frac{4}{5}\)</p>
<p>(c) \(\frac{6}{5}\)</p>
<p>(d) \(\frac{7}{5}\)</p>
Step-by-Step Solution
Key Concept: Rearrange the addition rule formula to solve for \(P(A) + P(B)\) given the union and intersection probabilities.
<p>Given: \(P(A \cup B) = \frac{3}{5}\) and \(P(A \cap B) = \frac{1}{5}\)</p><p>Using the addition rule: \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)</p><p>\(\frac{3}{5} = P(A) + P(B) - \frac{1}{5}\)</p><p>\(P(A) + P(B) = \frac{3}{5} + \frac{1}{5} = \frac{4}{5}\)</p>
Correct Answer: B