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A sample space consists of 9 elementary outcomes `E_(1),E_(2),…..,E_(9)` whose probabilities are `P(E_(1))=P(E_(2))=0.08,P(E_(3))=P(E_(4))=P(E_(5))=0.

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A sample space consists of 9 elementary outcomes E1,E2,…..,E9 whose probabilities are P(E1)=P(E2)=0.08,P(E3)=P(E4)=P(E5)=0.1 P(E6)=P(E1)=0.2,P(E8)=P(E9)=0.07 Suppose A={E1,E5,E8},B={E2,E5,E8,E9} (i) Calculate P(A), P(B) and P(A∩B) . (ii) Using the addition law of probability, calculate P(A∪B). (iii) List the composition of the event A∪B and calculate P(A∪B) by adding the probabilities of the elementary outcomes. Calculate P( - B ) from P(B), also calculate P( - B ) directly from the elementary outcomes of - B , Select the correct answer from above options

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Given S={E1,E2,E3,E4,E5,E6,E7,E8,E9} A={E1,E5,E8},B={E2,E5,E8,E9} P(E1)=P(E2)=0.08 P(E3)=P(E4)=P(E5)=0.1 P(E6)=P(E7)=2,P(E8)=P(E9)=0.07 (i) P(A)=P(E1)+P(E5)+P(E8) =0.08+0.1+0.07=0.25 (ii) P(A∪B)=P(A)+P(B)-P(A∩B) Now, P(B)=P(E2)+P(E5)+P(E8)+P(E9) =0.08+0.1+0.07+0.07=0.32 A∩B={E5,E8} P(A∩B)=P(E5)+P(E8)=0.1+0.7=0.17 On substituting these values in Eq. (i), we get P(A∪B)=0.25+0.32-0.17=0.40 (iii) A∪B={E1,E2,E5,E8,E9} P(A∪B)=P(E1)+P(E2)+P(E5)+P(E8)+P(E9) =0.08+0.08+0.1+0.07+0.07=0.40 (iv) ∵P - (B) =1-P(B)=1-0.32=0.68 and - B ={E1,E3,E4,E6,E7} (iv) ∵ P - (B) =P(E1)+P(E3)+P(E4)+P(E6)+P(E7) =0.08+0.1+0.1+0.2+0.2=0.68

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