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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)` ad `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

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

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`P(E_(1))=(1)/(4)`
`P_((E_(2))/(E_(1)))=(P(E_(1)capE_(2)))/(P(E_(1)))=(1)/(2)`
`P(E_(1)capE_(2))=(1)/(8)`
`P((E_(1))/(E_(2)))=(P(E_(1)capE_(2)))/(P_(E_(2)))=(1)/(4)`
`P(E_(2))=(1)/(2)`
`P_(E_(1)).P_(E_(2))=P(E_(1)capE_(2))`
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