If E and F are events such that P(E) = , P(F) = and P(E and F) = , find:(i) P(E or F), (ii) P(not E and not F).

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Solution

Given, Eand F are event such that,

P( E )= 1 4 P( F )= 1 2 P( E and F )= 1 8

(i)

The probability P( E or F )is,

P( E or F )=P( E )+P( F )−P( E and F ) = 1 4 + 1 2 − 1 8 = 2+4−1 8 = 5 8

(ii)

The probability P( not E and not F ) is,

P( E or F )=P( E∪F ) = 5 8 P( not E and not F )=P( E ′ ∩ F ′ ) =P ( E∪F ) ′

Further simplify.

P( not E and not F )=P ( E∪F ) ′ =1−P( E∪F ) =1− 5 8 = 3 8

Thus, P( not E and not F ) is 3 8 .

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