JEE Mains · Maths · STD 11 - 14. probability
Let \(A\) and \(B\) be two events such that the probability that exactly one of them occurs is \(\frac{2}{5}\) and the probability that \(A\) or \(B\) occurs is \(\frac{1}{2}\) then the probability of both of them occur together is
- A \(0.02\)
- B \(0.01\)
- C \(0.20\)
- D \(0.10\)
Answer & Solution
Correct Answer
(D) \(0.10\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-2 \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{2}{5}\) \(\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{2}\) \(\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{10}\)
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