Let E  be the event of committing an error in processing the form and let E _ 1, E _ 2 and E _ 3 be the events that Jayant, Sonia and Oliver processed the form. Find the value of _( i=1 ) ^3  P ( E _ i∣ E) .

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Now, 𝑷(𝑬_1∣𝑬) is Probability there is an error in processing the form, & Jayant processed the form 𝑷(𝑬_2∣𝑬) is Probability there is an error in processing the form, & Sonia processed the form 𝑷(𝑬_3∣𝑬) is Probability there is an error in processing the form, & Oliver processed the form Now, ∑_(𝑖=1)^3▒𝑃 (𝐸_𝑖│𝐸)=𝑃(𝑬_𝟏│𝑬)+𝑷(𝑬_𝟐│𝑬)+𝑷(𝑬_𝟑│𝑬) 𝑷(𝑬_3∣𝑬) is Probability there is an error in processing the form, & Oliver processed the form Now, ∑_(𝑖=1)^3▒𝑃 (𝐸_𝑖│𝐸)=𝑃(𝑬_𝟏│𝑬)+𝑷(𝑬_𝟐│𝑬)+𝑷(𝑬_𝟑│𝑬) = (𝑃(𝐸_1 ). 𝑃(𝐸|𝐸_1))/(𝑃(𝐸_1 ). 𝑃(𝐴|𝐸_1) + 𝑃(𝐸_2 ). 𝑃(𝐴|𝐸_2) + 𝑃(𝐸_3 ). 𝑃(𝐸|𝐸_1)) + (𝑃(𝐸_2 ). 𝑃(𝐸|𝐸_2))/(𝑃(𝐸_1 ). 𝑃(𝐸|𝐸_1) + 𝑃(𝐸_2 ). 𝑃(𝐸|𝐸_2) + 𝑃(𝐸_3 ). 𝑃(𝐸|𝐸_1)) + (𝑃(𝐸_3 ). 𝑃(𝐸|𝐸_3))/(𝑃(𝐸_1 ). 𝑃(𝐸|𝐸_1) + 𝑃(𝐸_2 ). 𝑃(𝐸|𝐸_2) + 𝑃(𝐸_3 ). 𝑃(𝐸|𝐸_1)) = (𝑃(𝐸_1 ). 𝑃(𝐸|𝐸_1) + 𝑃(𝐸_2 ). 𝑃(𝐸|𝐸_2) + 𝑃(𝐸_3 ). 𝑃(𝐸|𝐸_1))/(𝑃(𝐸_1 ). 𝑃(𝐸|𝐸_1) + 𝑃(𝐸_2 ). 𝑃(𝐸|𝐸_2) + 𝑃(𝐸_3 ). 𝑃(𝐸|𝐸_1)) = 1

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.