The accompanying Venn diagram shows three events, A, B and C and also the probabilities of the various intersections `["for instance", P (AcupB)=0.7].

Question

The accompanying Venn diagram shows three events, A, B and C and also the probabilities of the various intersections [ for instance , P ( A ∪ B ) = 0.7 ] . [ Determine (i) P (A) (ii) P ( B ∩ − C ) P (iii) P ( A ∪ B ) P (iv) P ( A ∩ − B ) P (v) P ( B ∩ C ) P (vi) Probability of exactly one of the three occurs. Select the correct answer from above options

Answer 1

Form the above Venn diagram, (i) P ( A ) = 0.13 + 0.07 = 0.20 P (ii) P ( B ∩ − C ) = P ( B ) − P ( B ∩ C ) = 0.07 + 0.10 + 0.15 − 0.15 = 0.07 + 0.10 = 0.17 P (iii) P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) P = 0.13 + 0.07 + 0.07 + 0.10 + 0.15 − 0.07 = = 0.13 + 0.07 + 0.10 + 0.15 = 0.45 = (iv) P ( A ∩ − B ) = P ( A ) − P ( A ∩ B ) = 0.13 + 0.07 = 0.13 P (v) P ( B ∩ C ) = 0.15 P (vi) P(exactly one of the three occurs) = 0.13 + 0.10 + 0.28 = 0.51 P(exactly one of the three occurs)