JEE Advanced 2013Paper 1
- Exam
- JEE Advanced
- Year
- 2013
- Paper
- Paper 1
- Subject
- Mathematics
- Chapter
- Probability
JEE Advanced 2013 · Paper 1 · Mathematics · Probability
Of the three independent events E_ 1 , E_ 2 and E_ 3 , the...
Of the three independent events {\text{E}_{1}, {\text{E}_{2} and {\text{E}_{3}, the probability that only {\text{E}_{1} occurs is , only {\text{E}_{2} occurs is and only {\text{E}_{3} occurs is . Let the probability that none of events {\text{E}_{1}, {\text{E}_{2} or {\text{E}_{3} occurs satisfy the equations \left(\alpha - 2 \beta\right) p = \alpha \beta. All the given probabilities are assumed to lie in the interval \left(\text{0, 1}\right)\dfrac{{\text{Probabilityoccurrence of E}_{1}}{{\text{Probability of occurrence of E}_{3}} =
Correct answer
6
Step-by-step solution
Let x, y, z be probability of E1, E2, E3 respectively
\to \text{x} \left(1 - \text{y}\right) \left(1 - \text{z}\right) = α
\to \text{y} \left(1 - \text{x}\right) \left(1 - \text{z}\right) = β
\to \text{z} \left(1 - \text{x}\right) \left(1 - \text{y}\right) = γ
Putting in the given relation we get x = 2y and y = 3z
\to \text{x} \left(1 - \text{y}\right) \left(1 - \text{z}\right) = α
\to \text{y} \left(1 - \text{x}\right) \left(1 - \text{z}\right) = β
\to \text{z} \left(1 - \text{x}\right) \left(1 - \text{y}\right) = γ
Putting in the given relation we get x = 2y and y = 3z