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Select the correct option from the given alternatives : The probability that a student knows the correct answer to a multiple choice question is 23 . If the student does not know the answer, t - Mathematics and Statistics

MCQ

Select the correct option from the given alternatives :

The probability that a student knows the correct answer to a multiple choice question is `2/3`. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is `1/4`. Given that the student has answered the question correctly, the probability that the student knows the correct answer is

Options

  • `5/6`

  • `6/7`

  • `7/8`

  • `8/9`

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Solution

`8/9`

Explanation:

Let event A: Student knows the correct answer.

event A': Student guesses the answer.

event B: Answer is correct

∴ P(A) = `2/3`, P(A') = `1/3, "P"("B"/"A'") = 1/4`

Clearly, `"P"("B"/"A")` = 1

Required probability = `"P"("A"/"B")`

= `("P"("A")*"P"("B"/"A"))/("P"("A")*"P"("B"/"A") + "P"("A'")"P"("B"/"A'"))`

= `(2/3 xx 1)/(2/3 xx 1 + 1/3 xx 1/4)`

= `8/9`

Concept: Concept of Probability
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 9 Probability
Miscellaneous Exercise 9 | Q I. (7) | Page 213
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