  Question

# A sample space consists of 9 elementary events E1,E2E3,....,E8,E9 whose probabilities are P(E1)=P(E2)=0.08, P(E3)=P(E4)=0.1, P(E6)=P(E7)=0.2 P(E8)=P(E9)=0.07 Suppose  A={E1,E5,E8}, B ={E2,E5,E8,E9} (i) Compute P(A),P(B), P(A∩B) (ii) Using the addition law of probability, find P(A∪B) (iii) List the composition of the even A∪B, and calculate P(A∪B) by adding the probabilities of the elementary events. (iv) Calculate P(¯¯¯¯B) from P(B), also calculate P(¯¯¯¯B) directly from the elementary events of ¯¯¯¯B

Solution

## Given,S =  {E1,E2,E3E4,E5,E6,E7,E8,E9} A = {E1,E5,E8}, B = {E2,E5,E8,E9} P(E1)=P(E2)=0.08, P(E3)=P(E4)=0.1, P(E6)=P(E7)=0.2 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)                                 ....(i) 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 ¯¯¯¯B={E1,E3,E4,E6,E7} ∴P(¯¯¯¯B)=P(E1)+P(E3)+P(E4)+P(E6)+P(E7) =0.08+0.1+0.1+0.2+0.2=0.68  Suggest corrections  Similar questions
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