In answering a question on a multiple choice test, a student eith… - Vidyadip

Question

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $\frac{3}{4}$ be the probability that he knows the answer and $\frac {1}{4}$ be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability $\frac{1}{4}$. What is the probability that the student knows the answer given that he answered it correctly?

✓

Answer

Let $E_1$ : the student knows the answer, then $, P(E_1) = \frac{3}{4}$
$E_2$ : the student guesses the answer, then $, P(E_2) = \frac{1}{4}$
Let $A$: the answer is correct.
$P(\frac {A}{{E_1}}) = 1, P(\frac {A}{{E_2}}) = \frac{1}{4}$
Hence, by Baye's theorm, we have,
$P(\frac {E_1}{A}) = \frac{{P({E_1})P(A/{E_1})}}{{P({E_1})P(A/{E_1}) + P({E_2})P(A/{E_2})}}$
$ = \frac{{1 \times \frac{3}{4}}}{{1 \times \frac{3}{4} + \frac{1}{4} \times \frac{1}{4}}} = \frac{{12}}{{13}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Probability→Probability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\limits^{1}_02^{\text{x}-[\text{x}]}\text{dx}$

Symmetric and transitive but not reflexive.

Find the rate of change of the volume of a sphere with respect to its surface area when the radius is 2cm.

Find:
$\int \frac{\text{dx}}{\sqrt{3 - \text{2x - x}^{2}}}$

Construct a $2 \times 2$ matrix $A = [a_{ij}]$ whose elements $a_{ij}$ are give by: $\frac{(\text{i}+\text{j})^2}{2}$

Evaluate $\begin{vmatrix}\cos\alpha\cos\beta&\cos\alpha\sin\beta&-\sin\alpha\\-\sin\beta&\cos\beta&0\\\sin\alpha\cos\beta&\sin\alpha\sin\beta&\cos\alpha\end{vmatrix}.$

Construct a 3 × 4 matrix, whose elements are given by:$\text{a}_{\text{ij}}=\frac{1}{2} \left|-3{\text{i}+\text{j}}\right| $

Find x, y, a and b if $\begin{bmatrix}3\text{x}+4\text{y}&2&\text{x}-2\text{y}\\\text{a}+\text{b}&2\text{a}-\text{b}&^-1\end{bmatrix}=\begin{bmatrix}2&2&4\\5&-5&-1\end{bmatrix}$

For any two vectors $\vec{\text{a}} $ and $\vec{\text{b}},$ write when $\big|\vec{\text{a}}+\vec{\text{b}}\big|=|\vec{\text{a}}|+\big|\vec{\text{b}}\big|$ holds.

Let * be a binary operation on N given by a * b = HCF (a, b), a, b ∈ N. Write the value of 22 * 4.