Question

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].` Determine
(i) P (A)
(ii) `P (Bcapoverset(-)C)`
(iii) `P (AcupB)`
(iv) `P (Acapoverset(-)B)`
(v) `P (BcapC)`
(vi) Probability of exactly one of the three occurs.

Answer 1

Form the above Venn diagram,
(i) `P(A)=0.13+0.07=0.20`
(ii) `P(Bcapoverset(-)C)=P(B)-P(BcapC)=0.07+0.10+0.15-0.15=0.07+0.10=0.17`
(iii) `P(AcupB)=P(A)+P(B)-P(AcapB)`
`=0.13+0.07+0.07+0.10+0.15-0.07`
`=0.13+0.07+0.10+0.15=0.45`
(iv) `P(Acapoverset(-)B)=P(A)-P(AcapB)=0.13+0.07=0.13`
(v) `P(BcapC)=0.15`
(vi) `"P(exactly one of the three occurs)"=0.13+0.10+0.28=0.51`