# 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

• 5/6

• 6/7

• 7/8

• 8/9

#### Solution

8/9

Explanation:

Let event A: Student knows the correct answer.

event A': Student guesses the answer.

∴ 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