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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?
  1. E1 and E2 are mutually independent events
  2. E1 and E2 are exhaustive events
  3. E2 is twice as likely to occur as E1
  4. P(E1E2),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(E1E2),P(E1),P(E2) are in G.P
P(E2E1)=P(E1E2)P(E1)P(E1E2)=18P(E2)=18P(E1E2)=12P(E1)P(E2)=14×12=P(E1E2) & P(E1E2)=58
So E1 & E2 are independent but not exhaustive set of events

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