In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let 3/5 be the probability that he knows the answer and 2/5 be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability 1/5. Let E 1 , E 2 , E be the events that the student knows the answer, guesses the answer and answers correctly respectively.
In answering a question on a multiple - Teachoo.jpg

Based on the above information, answer the following:

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Question 1

What is the value of P(E1)?

(a) 2/5 

(b) 1/3 

(c) 1 

(d) 3/5

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Question 2

Value of P(E | E1) is

(a) 1/3   

(b) 1 

(c) 2/3   

(d) 4/5

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Question 3

∑_(k=1)^(k=2)▒γ€–P(E│E_k )  P(E_k ) γ€—   Equal

(a) 11/15 

(b) 4/15 

(c) 1/5 

(d) 1

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Question 4

Value of ∑_(k=1)^(k=2)▒γ€– P(E_k ) γ€—

(a) 1/3 

(b) 1/5 

(c) 1 

(d) 3/5

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Question 5

What is the probability that the student knows the answer given that he answered it correctly?

(a) 2/11 

(b) 5/3  

(c) 9/11 

(d) 13/3

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Transcript

Question In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let 3/5 be the probability that he knows the answer and 2/5 be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability 1/3. Let E1, E2, E be the events that the student knows the answer, guesses the answer and answers correctly respectively. Based on the above information, answer the following:Given E1 : Student knows the answer E2 : Student guesses the answer E : Student answers correctly Now, P("E1") = P(student knows the answer) = πŸ‘/πŸ“ P(E2) = P(student guesses the answer) = 𝟐/πŸ“ Also, Given that assume that a student who guesses at the answer will be correct with probability 1/3 i.e. P(answer correct | he guesses) ∴ P(E | E2) = 1/3 Question 1 What is the value of P(E1)? (a) 2/5 (b) 1/3 (c) 1 (d) 3/5P(E1) = πŸ‘/πŸ“ So, the correct answer is (d) Question 2 Value of P(E | E1) is (a) 1/3 (b) 1 (c) 2/3 (d) 4/5 P(E | E1) = P( student answer correct | he knows answer) = Probability that student answers correctly, if he knows the answer = 1 So, the correct answer is (b) Question 3 βˆ‘_(π‘˜=1)^(π‘˜=2)▒〖𝑃(𝐸│𝐸_π‘˜ ) 𝑃(𝐸_π‘˜ ) γ€— Equal (a) 11/15 (b) 4/15 (c) 1/5 (d) 1 βˆ‘_(π‘˜=1)^(π‘˜=2)▒〖𝑃(𝐸│𝐸_π‘˜ ) 𝑃(𝐸_π‘˜ ) γ€— = 𝑃(𝐸│𝐸_1 ) 𝑃(𝐸_1 )+ 𝑃(𝐸│𝐸_2 ) 𝑃(𝐸_2 ) = πŸΓ—πŸ‘/πŸ“+𝟏/πŸ‘Γ—πŸ/πŸ“ = 3/5Γ—2/15 = 𝟏𝟏/πŸπŸ“ So, the correct answer is (a) Question 4 Value of βˆ‘_(π‘˜=1)^(π‘˜=2)β–’γ€– 𝑃(𝐸_π‘˜ ) γ€— (a) 1/3 (b) 1/5 (c) 1 (d) 3/5 βˆ‘_(π‘˜=1)^(π‘˜=2)▒𝑃(𝐸_π‘˜ ) = 𝑃(𝐸_1 ) + 𝑃(𝐸_2 ) = 3/5+2/5 = 1 So, the correct answer is (c) Question 5 What is the probability that the student knows the answer given that he answered it correctly? (a) 2/11 (b) 5/3 (c) 9/11 (d) 13/3 We need to find the Probability that the student knows the answer given that he answered it correctly i.e. P(𝐸_1 "|E") Now, "P(" 𝑬_𝟏 "|E) = " (𝑃(𝐸_1 ). 𝑃(𝐸|𝐸_1))/(𝑃(𝐸_1 ). 𝑃(𝐸|𝐸_1 ) + 𝑃(𝐸_2 ). 𝑃(𝐸|𝐸_2 ) ) So, "P(" 𝑬_𝟏 "|E) = " (𝑃(𝐸_1 ). 𝑃(𝐸|𝐸_1))/(𝑃(𝐸_1 ). 𝑃(𝐸|𝐸_1 ) + 𝑃(𝐸_2 ). 𝑃(𝐸|𝐸_2 ) ) = (3/5 Γ— 1)/(3/5 Γ— 1 + 2/5 Γ— 1/3 ) = 3/5Γ—15/11 = πŸ—/𝟏𝟏 So, the correct answer is (c)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.