Q. 8

# If E1

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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