CUET · MATHS · PYQ PAPER 2023
Two events \(E\) and \(F\) are independent. If \(P(E)=0.3, P(E \cup F)=0.5\), then \(P(E / F)-P(F / E)\) equals :
- A \(\frac{2}{7}\)
- B \(\frac{3}{35}\)
- C \(\frac{1}{70}\)
- D \(\frac{1}{7}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{70}\)
Step-by-step Solution
Detailed explanation
\(P(E \cup F) = P(E) + P(F) - P(E)P(F)\) \(0.5 = 0.3 + P(F) - 0.3P(F)\) \(0.2 = 0.7P(F)\) \(P(F) = \frac{0.2}{0.7} = \frac{2}{7}\) \(P(E / F) = P(E) = 0.3 = \frac{3}{10}\) (for independent events) \(P(F / E) = P(F) = \frac{2}{7}\) (for independent events)…
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