Question

If E1 and E2 are two events such that P(E1)=14,P(E2E1)=12 and P(E1E2)=14, then which of the following is/are correct?

- E1 and E2 are mutually independent events
- E1 and E2 are exhaustive events
- E2 is twice as likely to occur as E1
- P(E1∩E2),P(E1),P(E2) are in G.P

Solution

The correct options are

**A** E1 and E2 are mutually independent events

**C** E2 is twice as likely to occur as E1

**D** P(E1∩E2),P(E1),P(E2) are in G.P

P(E2E1)=P(E1∩E2)P(E1)⇒P(E1∩E2)=18⇒P(E2)=18P(E1E2)=12P(E1)P(E2)=14×12=P(E1∩E2) & P(E1∪E2)=58

So E1 & E2 are independent but not exhaustive set of events

P(E2E1)=P(E1∩E2)P(E1)⇒P(E1∩E2)=18⇒P(E2)=18P(E1E2)=12P(E1)P(E2)=14×12=P(E1∩E2) & P(E1∪E2)=58

So E1 & E2 are independent but not exhaustive set of events

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