JEE Mains · Maths · STD 12 - 13. probability
Let \(A, B\) and \(C\) be three events such that the probability that exactly one of \(A\) and \(B\) occurs is \((1-k)\), the probability that exactly one of \(B\) and \(C\) occurs is \((1-2 k)\), the probability that exactly one of \(C\) and \(A\) occurs is \((1-k)\) and the probability of all \(A, B\) and \(C\) occur simultaneously is \(k^{2}\), where \(0\,<\,\mathrm{k}\,<\,1\). Then the probability that at least one of \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) occur is:
- A greater than \(\frac{1}{2}\)
- B greater than \(\frac{1}{4}\) but less than \(\frac{1}{2}\)
- C exactly equal to \(\frac{1}{2}\)
- D greater than \(\frac{1}{8}\) but less than \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(A) greater than \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}(\overrightarrow{\mathrm{A}} \cap \mathrm{B})+\mathrm{P}(\mathrm{A} \cap \overline{\mathrm{B}})=1-K\) \(\mathrm{P}(\overrightarrow{\mathrm{A}} \cap \mathrm{C})+\mathrm{P}(\mathrm{A} \cap \bar{C})=1-2 k\)…
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