Algebra

Probability

Hard

These days competitive examinations are held in online mode. During the examination student either guesses or copies or knows the answer of a multiple choice question (MCQ) with four choices each. The probability that a student makes guesses is $\frac{1}{3}$ and that he/she copies $\frac{1}{6}$ . The probability of marking answer correctly when he/she copied is $\frac{1}{8}$ and probability of making answer correctly when he/she guesses is $\frac{1}{4}$ . It is also assumed that a student marked answer correctly if he/she knows the answer.

By using the above mentioned information answer following question.

The probability that a student knows the answer, is:

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{5}{6}$

$1$

✅ Correct Option: 2

Let $K, G, C$ be events that student knows, guesses, copies respectively. These are exhaustive: $P(K) + P(G) + P(C) = 1$ . So $P(K) = 1 - \frac{1}{3} - \frac{1}{6} = \frac{6-2-1}{6} = \frac{3}{6} = \frac{1}{2}$ .

Question 42

If answer is correct, the probability that he guesses, is :

Question 43

The conditional probability that his answer is correct when it is given that he knew it :

Question 44

The probability of answering a question correctly, is :

Question 45

The probability that he copied it given that his answer is correct :

The probability that a student knows the answer, is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)