Home
Class 12
MATHS
If E(1) and E(2) are two events such tha...

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

A

then `E_(1)` and `E_(2)` are independent

B

`E_(1)` and `E_(2)` are exhaustive

C

`E_(2)` is twice as likely to occur as `E_(1)`

D

Probabilites of the events `E_(1) nn E_(2)`, `E_(1)` and `E_(2)` are in `G.P.`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`(a,c,d)` `P(E_(2)//E_(1))=(P(E_(1)nnE_(2)))/(P(E_(1)))`
`(1)/(2)=(P(E_(1)nnE_(2)))/(1//4)`
`impliesP(E_(1)nnE_(2))=(1)/(8)=P(E_(2))*P(E_(1)//E_(2))`
`=P(E_(2))*(1)/(4)`
`impliesP(E_(2))=(1)/(2)`
Since `P(E_(1) nnE_(2))=(1)/(8)=P(E_(1))*P(E_(1))*P(E_(2))`, events are independent
Also `P(E_(1)uuE_(2))=(1)/(2)+(1)/(4)-(1)/(8)=(5)/(8)`
`impliesE_(1)` and `E_(2)` are not exhaustive.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    CENGAGE|Exercise Single correct Answer|46 Videos

  • PROBABILITY

    CENGAGE|Exercise Comprehension|2 Videos

  • PROBABILITY

    CENGAGE|Exercise Comprehension|2 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE|Exercise Exercise|9 Videos

  • PROBABILITY AND STATISTICS

    CENGAGE|Exercise Question Bank|24 Videos

Similar Questions

Explore conceptually related problems

If E and F are independent events, show that P(EuuF) =1- P(E') P(F') .

If E and F are independent events such that P(E')=0.2 and P(F')=0.5, find P(EnnF)

If E and F are events such that P(E) = 1/4, P(F) = 1/2 and P(E and F) = 1/8 , find (i) P(E or F), (ii) P(not E and not F).

E and F are events such that P(E) =(1)/(3) , P(F)= (1)/(5), P(E uu F)= (11)/(50) . Find i. P(E|F) ii. P(F|E).

E and F are events such that P(E) =(1)/(3) P(F)= (1)/(4) , P(EnnF) = (1)/(5) . Find i. P(E|F) ii. P(F|E) iii. P(E uuF)

If E(x)=1/2, E(x^(2))=1/4 then var(x) is

Given that E and F are events such that P(E)= 0.6, P(F) = 0.3 and P(Enn F) = 0.2 , find P(E|F) and P(F|E)

A sample space consists of 9 elementary outcomes outcomes E_(1), E_(2) ,…, E_(9) whose probabilities are: P(E_(1))=P(E_(2)) = 0.09, P(E_(3))=P(E_(4))=P(E_(5))=0.1 P(E_(6)) = P(E_(7)) = 0.2, P(E_(8)) = P(E_(9)) = 0.06 If A = {E_(1), E_(5), E_(8)}, B= {E_(2), E_(5), E_(8), E_(9)} then (a) Calculate P(A), P(B), and P(A nn B). (b) Using the addition law of probability, calculate P(A uu B) . (c ) List the composition of the event A uu B , and calculate P(A uu B) by adding the probabilities of the elementary outcomes. (d) Calculate P(barB) from P(B), also calculate P(barB) directly from the elementarty outcomes of B.

Let E and F be events with P(E) = (3)/(5), P(F)= (3)/(10) and P(EnnF)= (1)/(5) Are E and F independent?

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(Ecap F) = 0.2 , find P(E|F) and P(F|E).