Question

We have:

                    P(A) = 0.75

                    P(B|A) = 0.9

                    P(B|A′) = 0.8

                    P(C|A ∩ B) = 0.8

                    P(C|A ∩ B′) = 0.6

                    P(C|A′ ∩ B) = 0.7

                    P(C|A′ ∩ B′) = 0.3     

Compute:

              a) ?(?′| ?′)

              b) P (?′ ∪ ?′)

              c) ?(? ∩ ? ∩ ?)

              d) P(C)

              e) ?(? ∩ ? ∩ ?)’

              f) P(B)

              g) P(AUBUC)

Answer 1

a)

b)

By the complement rule,

So,

By the law of total probability

By the Demorgan's law

c)

So,

(d)

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So,

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