Algebra

Probability

Medium

CASE STUDY

In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let $\frac{3}{5}$ be the probability that he knows the answer and $\frac{2}{5}$ be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability $\frac{1}{3}$ . Let $E_1$ , $E_2$ , and E be the events that the student knows the answer, guesses the answer and answers correctly respectively. A student answers correctly if he/she knows the answer. Using the above information, answer the question:

The probability of 'the student knows the answer given that he answered it correctly' is

$\frac{2}{11}$

$\frac{5}{3}$

$\frac{9}{11}$

$\frac{3}{13}$

✅ Correct Option: 3

By Bayes' theorem: $P(E_1/E) = \frac{P(E_1) P(E/E_1)}{P(E)} = \frac{(3/5)(1)}{11/15} = \frac{3/5 \cdot 15}{11} = \frac{9}{11}$ .

Question 46

The value of $P(E/E_1)$ is

Question 47

The value of $P(E)$ is

Question 48

The probability that a question is guessed by a student and found to be correct is.

Question 50

It is given that student marked the answer correctly, the probability that he guesses is

The probability of 'the student knows the answer given that he answered it correctly' is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)