Algebra

Probability

Medium

core

Probability that a man speaks truth is $\frac{3}{4}$ . He throws a die and reports that it is a six. The probability that it is actually a six is

$\frac{1}{3}$

$\frac{3}{8}$

$\frac{5}{8}$

$\frac{2}{3}$

✅ Correct Option: 2

Let $E_1$ = die actually shows a six, $E_2$ = die does not show a six, and $A$ = man reports that it is a six.

$P(\text{truth}) = \dfrac{3}{4}$

$P(\text{lies}) = 1 - \dfrac{3}{4} = \dfrac{1}{4}$

$P(E_1) = \dfrac{1}{6}$

$P(E_2) = \dfrac{5}{6}$

If the die is a six, the man reports six only when he speaks truth:

$P(A|E_1) = \dfrac{3}{4}$

If the die is not a six, the man reports six only when he lies:

$P(A|E_2) = \dfrac{1}{4}$

Using Bayes' Theorem:

$P(E_1|A) = \dfrac{P(A|E_1) \cdot P(E_1)}{P(A|E_1) \cdot P(E_1) + P(A|E_2) \cdot P(E_2)}$

$= \dfrac{\frac{3}{4} \times \frac{1}{6}}{\frac{3}{4} \times \frac{1}{6} + \frac{1}{4} \times \frac{5}{6}}$

$= \dfrac{\frac{3}{24}}{\frac{3}{24} + \frac{5}{24}}$

$= \dfrac{\frac{3}{24}}{\frac{8}{24}}$

$= \dfrac{3}{8}$

The probability that it is actually a six is $\boxed{\dfrac{3}{8}}$

2025: 26 May Shift 2

If A and B are two distinct events such that P(A|B) = P(B|A), then which of the following is /are possible?

(A) A= B

(B) P (A) = P(B)

(D) A∩ B = ɸ

Choose the correct answer from the options given below:

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If $a > 0$ , then $P(0 < x \leq 2)$ is equal to

2025: 27 May Shift 1

Let box I contains 3 black and 4 white balls, box II contains 2 black and 2 white balls, box III contains 4 black and 3 white balls. A box is selected at random and then a ball is randomly drawn from the selected box. If the color of the ball is black then the probability that the ball is drawn from box III, is:

2025: 13 May Shift 1

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Probability that a man speaks truth is 34\frac{3}{4}43​. He throws a die and reports that it is a six. The probability that it is actually a six is

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CUET Mathematics Past Year Questions (Topic-Wise)

Probability that a man speaks truth is $\frac{3}{4}$ . He throws a die and reports that it is a six. The probability that it is actually a six is