Home
Class 12
MATHS
Let E(1) and E(2) be two events such tha...

Let `E_(1)` and `E_(2)` be two events such that `P(E_(1))=0.3, P(E_(1) uu E_(2))=0.4` and `P(E_(2))=x`. Find the value of x such that
(i) `E_(1)` and `E_(2)` are mutually exclusive,
(ii) `E_(1)` and `E_(2)` are independent.

Text Solution

Verified by Experts

(i) Let `E_(1)` and `E_(2)` be mutially exclusive. Then `E_(1) nn E_(2)= varphi`.
`:. P(E_(1) uu E_(2))=P(E_(1))+P(E_(2))`
`implies 0.4=0.3+x`
`implies x=0.1`
Thus, when `E_(1)` and `E_(2)` mutually exclusive, then `x=0.1`.
(ii) Let `E_(1)` and `E_(2)` be two independent events. Then.
`P(E_(1) nn E_(2))=P(E_(1))xxP(E_(2))=0.3xx x=0.3 x`.
`:. P(E_(1) uu E_(2))=P(E_(1))+P_(E_(2))-P(E_(1) nn E_(2))`
`implies 0.4=0.3+x-0.3 x`
`implies 0.7 x=0.1`
`implies x=0.1/0.7=1/7`
Thus, when `E_(1)` and `E_(2)` are independent, then `x=1/7`.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RS AGGARWAL|Exercise Exercise 29A|17 Videos

  • PROBABILITY

    RS AGGARWAL|Exercise Exercise 29B|23 Videos

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise Objective Questions Ii|56 Videos

  • PROBABILITY DISTRIBUTION

    RS AGGARWAL|Exercise Exercise 32|32 Videos

Similar Questions

Explore conceptually related problems

Let E_(1) and E_(2) are the two independent events such that P(E_(1))=0.35 and P(E_(1) uu E_(2))=0.60 , find P(E_(2)) .

If E_(1) and E_(2) are two events such that P(E_(1))=1//4 , P(E_(2)//E_(1))=1//2 and P(E_(1)//E_(2))=1//4 , then

For two events E_(1) and E_(2),P(E_(1))=(1)/(2),P(E_(1)uu E_(2))=(3)/(5) and P(E_(2))=p. Find p in the following cases.(i) when E_(1) and E_(2) are mutually exclusing events. (ii) E_(1) and E_(2) are independent events

If E_(1) and E_(2) be two events such that P(E_(1))=0.3, P(E_(2))=0.2 and P(E_(1)nnE_(2))=0.1, then find: (i) P(barE_(1)nnE_(2)) (ii) P(E_(1)nnbarE_(2))

Let E_(1) and E_(2) be the events such that P(E_(1))=1/3 and P(E_(2))=3/5 . Find : (i) P(E_(1)uuE_(2)) , where E_(1) and E_(2) are mutually ecclusive, (ii) P(E_(1) nn E_(2)) , when E_(1) and E_(2) are independent.

If E_(1) and E_(2) are two independent events such that P(E_(1))=0.3 and P(E_(2))=0.6 Then find the value of the given expressions

If E_(1) and E_(2), are two events such that P(E_(1))=(1)/(4),P(E_(2))=(1)/(4)*(a) then E_(1) and E_(2), are independent

E_(1) and E_(2) be two mutually exclusive events such that P(E_(1))=(4)/(7) and P(E_(2))=(1)/(7) . The value of P(E_(1) or E_(2)) .

E_(1) and E_(2) be two mutually exclusive events such that P(E_(1))=(4)/(7) and P(E_(2))=(1)/(7) . The value of P(E_(1) or E_(2)) .

If E_(1) and E_(2) are the two events such that P(E_(1))=1/4, P(E_(2))=1/3 and P(E_(1) uu E_(2))=1/2 , show that E_(1) and E_(2) are independent events.