Given P(A ⋂ B) = 0.07
From the given Venn Diagram
(a) P(A)
= 0.07 + 0.10 + 0.15 – 0.15
= 0.07 + 0.10
= 0.17
(c) P(A ⋃ B)
By General Addition Rule,
P(A ⋃ B) = P(A) + P(B) – P(A ⋂ B)
⇒ P(A ⋃ B) = 0.20 + (0.07 + 0.10 + 0.15) – 0.07
⇒ P(A ⋃ B) = 0.20 + 0.25
⇒ P(A ⋃ B) = 0.45
= 0.20 – 0.07 [from part (a)]
= 0.13
(e) P(B ⋂ C)
P(B ⋂ C) = 0.15
(f) Probability of exactly one of the three occurs
P(exactly one of the three occurs) = 0.13 + 0.10 + 0.28
= 0.51