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Answer. Venn Diagrams. ε = 100% . A represents owning a car. B represents owning an air conditioner. B = 94%. A = 92%. 87%. 92% - 87% = 5%. 94% - 87% = 7%. P(A u B) = 99% P(A u B) ′ = 1% P(A ′ n B) = 7%. Answer. Venn Diagrams. ε = 100% . H represents history.
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Answer Venn Diagrams ε = 100% A represents owning a car. B represents owning an air conditioner. B = 94% A = 92% 87% 92% - 87% = 5% 94% - 87% = 7% • P(A u B) = 99% • P(A u B) ′ = 1% • P(A ′ n B) = 7%
Answer Venn Diagrams ε = 100% H represents history. M represents maths. M = 50% H = 35% 35%+ 50% - 70% = 15% 35% - 15% = 20% 50% - 15% = 35% 100% - 30% = 70% H′nM′ = 30% • P(H u M) = 100% - 30% = 70% • Use P(H u M) = P(H) + P(M) – P(H n M)P(H n M) = 35% + 50% - 70% = 15% • P( only one of the subjects) = ( P(H) – P(H n M) ) + ( P(M) – P(H n M) ) • = ( 35% - 15% ) + ( 50% - 15% ) = 55%
Answer Venn Diagrams ε = 1 A = first light red B = second light red B = 0.6 A = 0.7 0.4 0.7 – 0.4 = 0.3 0.6 – 0.4 = 0.2 • P(A u B) = 0.9 • P(A u B)’ = 0.1 • P(A’ n B) = 0.2
Answer Venn Diagrams ε = 100% A = jury convicts B = judge convicts B = 73% A = 67% • P(A n B′) = 67% - 46% = 21% • P(A′ n B) = 73% - 46% = 27% • P(A n B′) + P(A′ n B) = 21% + 27%= 48% • 100% – (A u B) (A u B) = (A) + (B) – ( A n B ) • = 67% + 73% – 46% • = 94% • The percentage neither the panel nor the judge would convict = 100% – 94% = 6% 46% 67% - 46% = 21% 73% - 46% = 27% 67% + 73% – 46% = 94% 100% - 94% = 6%
