WBJEE · Maths · Probability
A and \(\mathrm{B}\) are independent events. The probability that both A and \(\mathrm{B}\) occur is \(\frac{1}{20}\) and the probability that neither of them occurs is \(\frac{3}{5}\). The probability of occurrence of \(\mathrm{A}\) is
- A \(\frac{1}{2}\)
- B \(\frac{1}{10}\)
- C \(\frac{1}{4}\)
- D \(\frac{1}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{5}\)
Step-by-step Solution
Detailed explanation
\(P(A \cap B)=P(A) P(B)=\frac{1}{20} \Rightarrow P(B)=\frac{1}{2 O P(A)}\) \(P(\bar{A} \cap \bar{B})=\frac{3}{5}=1-P(A \cup B)\) \(\Rightarrow \frac{3}{5}=1-P(A)-P(B)+P(A \cap B)\) \(\Rightarrow \frac{3}{5}=1-P(A)-\frac{1}{20 P(A)}+\frac{1}{20}\)…
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