Probability
Union and Complement
Grade 12
Question:
<p>If the probability that E or F happens is 1 and the probability that neither E nor F happens is \(\frac{1}{2}\), then find \(P(E)\) and \(P(F)\)</p>
<p>(a) \(P(E) = \frac{1}{3}, P(F) = \frac{1}{4}\)</p>
<p>(b) \(P(E) = \frac{1}{2}, P(F) = \frac{1}{6}\)</p>
<p>(c) \(P(E) = \frac{1}{12}, P(F) = \frac{1}{3}\)</p>
<p>(d) \(P(E) = \frac{1}{3}, P(F) = \frac{1}{2}\)</p>
Step-by-Step Solution
Key Concept: Use the complement rule: P(E or F) + P(neither E nor F) = 1, and solve using P(E or F) = P(E) + P(F) - P(E and F).
<p>Not provided in source text</p>
Correct Answer: a