If E1 and E2 are the two events such that and show that E1 and E2 are independent events.

Given: E1 and E2 are two events such that P(E1) = and P(E2) = and


P(E1 E2) =


To show: E1 and E2 are independent events.


We know that,


Hence, P(E1 E2) = P(E1) + P(E2) - P(E1 E2)


= + -


= Equation 1


Since The condition for two events to be independent is


P(E1 E2) = P(E1) P(E2)


=


= Equation 2


Since, Equation 1 = Equation 2


E1 and E2 are independent events.


Hence proved.


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