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.
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