JEE Mains · Maths · STD 12 - 13. probability
Let there be three independent events \(E _{1}, E _{2}\) and \(E _{3}\). The probability that only \(E _{1}\) occurs is \(\alpha\), only \(E _{2}\) occurs is \(\beta\) and only \(E _{3}\) occurs is \(\gamma .\) Let \('p'\) denote the probability of none of events occurs that satisfies the equations \((\alpha-2 \beta) p =\alpha \beta\) and \((\beta-3 \gamma) p =2 \beta \gamma .\) All the given probabilities are assumed to lie in the interval \((0,1)\) Then, \(\frac{\text { Probability of occurrence of } E _{1}}{\text { Probability of occurrence of } E _{3}}\) is equal to ..........
- A \(8\)
- B \(6\)
- C \(3\)
- D \(9\)
Answer & Solution
Correct Answer
(B) \(6\)
Step-by-step Solution
Detailed explanation
Let \(P \left( E _{1}\right)= P _{1} ; P \left( E _{2}\right)= P _{2} ; P \left( E _{3}\right)= P _{3}\) \(P \left( E _{1} \cap \overline{ E }_{2} \cap \overline{ E }_{3}\right)=\alpha= P _{1}\left(1- P _{2}\right)\left(1- P _{3}\right) \ldots \ldots\)…
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