Home
Class 12
MATHS
Of the three independent event E(1),E(2)...

Of the three independent event `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`. If the probavvility p that none of events `E_(1), E_(2)` or `E_(3)` occurs satisfy the equations `(alpha - 2beta)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, `("probability of occurrence of " E_(1))/("probability of occurrence of " E_(3))` is equal to

A

`(6)/(1)`

B

`(1)/(3)`

C

`(1)/(2)`

D

`(1)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let x, y and z be probability of occurrence of `E_(1), E_(2)` and `E_(3)`, respectively.
Then, `alpha=x(1-y) (1-z)` …(i)
`beta = (1-x) .y(1-z)` …(ii)
`gamma = (1-x) (1-y)z` …(iii)
and `p=(1-x) (1-y) (1-z)` …(iv)
Given, `(alpha - 2beta) p = alpha beta` and `(beta - 3gamma) p = 2 beta gamma` ...(v)
From the above equations, we get
`x = 2y`
and `y = 3z`
`therefore " " x = 6z`
`rArr (x)/(z)=6`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PRACTICE EXERCISE (Exercies 2 (MISCELLANEOUS PROBLEMS))|30 Videos

  • PROBABILITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 1 (TOPICAL PROBLEMS)|44 Videos

  • PRACTICE SET 24

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathmatics)|50 Videos

  • SEQUENCES AND SERIES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 31|1 Videos

Similar Questions

Explore conceptually related problems

Of the 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 the probability p that none of events E_1, E_2 and E_3 occurs satisfy the equations (alpha-2beta), p=alphabeta and (beta-3gamma) p=2beta gamma. All the given probabilities are assumed to lie in the interval (0,1). Then,(probability of occurrence of E_1) / (probability of occurrence of E_3) is equal to

If E and F are independent events, P(E)=(1)/(2) and P(F)=(1)/(3) , then P(E nn F) is :

The Probability that at least one of the events E_(1) and E_(2) will occur is 0.6. If the probability of their occurrence simultaneously is 0.2, then find P(barE_(1))+P(barE_(2))

For any two independent events E_(1) and E_(2)P{(E_(1)uu E_(2))nn(E_(1)nn E_(2)} is

The angles alpha , beta , gamma of a triangle satisfy the equations 2 sin alpha + 3 cos beta = 3sqrt(2) and 3sin beta + 2cos alpha = 1 . Then angle gamma equals

If alpha, beta and gamma are the roots of the equation x^(3)+x+2=0 , then the equation whose roots are (alpha- beta)(alpha-gamma), (beta-gamma)(beta-gamma) and (gamma-alpha)(gamma-alpha) is

If alpha, beta, gamma be the zeros of the polynomial p(x) such that (alpha+beta+gamma) = 3, (alpha beta+beta gamma+gamma alpha) =- 10 and alpha beta gamma =- 24 then p(x) = ?

The probabilities of the occurrences of two events E_(1) and E_(2) are 0.25 and 0.50 respectively. The probability of their simultaneous occurrence is 0.14. Find the probability that neither E_(1) " nor " E_(2) occurs.