a PEC b PE F c PE F d PEC FC e PE FC Solutiona PEc 1

(a)	P(EC) =
(b)	P(E F) =
(c)	P(E F) =
(d)	P(EC FC) =
(e)	P(E FC) =

Solution

a)

P(Ec) = 1 - P(E) = 1- 0.57 = 0.43 [answer]

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b)

P(E n F) = P(E) +P(F) - P(E U F)

As

P(E U F) = P(Ec n F) + P(E) = 0.21+0.57 = 0.78,

P(E n F) = P(E) +P(F) - P(E U F)

P(E n F) = 0.57+0.34-0.78 = 0.13 [answer]

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c)

P(E U F) = 0.78 as in part B. [answer]

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d)

P(Ec n Fc) = P (E U F)c = 1 - P(E U F) = 0.22 [answer]

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e)

P(E U Fc) = 1 - [P(F) - P(E n F)] = 1 - [0.34-0.13] = 0.79 [answer]