Algebra

Probability

Easy

common

A die is rolled thrice. What is the probability of getting a number greater than $4$ in the first and the second throw of dice and a number less than $4$ in the third throw ?

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{1}{9}$

$\frac{1}{18}$

✅ Correct Option: 4

On a standard die with faces numbered $1$ through $6$ :

Numbers greater than $4$ : $5, 6$ (total $2$ possibilities)

Numbers less than $4$ : $1, 2, 3$ (total $3$ possibilities)

For each throw:

Probability of getting a number $> 4 = \dfrac{2}{6} = \dfrac{1}{3}$

Probability of getting a number $< 4 = \dfrac{3}{6} = \dfrac{1}{2}$

Since all throws are independent events, we multiply the individual probabilities:

Probability = $\dfrac{1}{3} \times \dfrac{1}{3} \times \dfrac{1}{2}$

$= \dfrac{1}{18}$

2022: 10 Aug Shift 1

A man is known to speak truth 4 out of 5 times. He throws a die and reports that five appears. Then the probability that actual five appears on the dice is

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There are two bags. Bag-1 contains $4$ white and $6$ black balls and Bag-2 contains $5$ white and $5$ black balls. A die is rolled, if it shows a number divisible by 3, a ball is drawn from Bag-1, else a ball is drawn from Bag-2. If the ball drawn is not black in colour, the probability that it was not drawn from Bag-2 is :

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A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$ . They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases.

The probability that seed is not of type $A_1$ , given that seed germinates.

2026: 26 May Shift 2

A random variable $X$ has the following probability distribution:

X	0	1	2	3	4
P(X)	0	$\dfrac{k}{2}$	$\dfrac{3k}{2}$	$\dfrac{k}{3}$	$2k$

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Value of $k$	I.	$\dfrac{7}{13}$
B.	Value of $P(X \leq 3)$	II.	$\dfrac{3}{26}$
C.	Value of $P(X > 1)$	III.	$\dfrac{23}{26}$
D.	Value of $P(X < 2)$	IV.	$\dfrac{3}{13}$

Choose the correct answer from the options given below:

2025: 27 May Shift 1

Let X be a random variable. Let E (X) and Var (X) denote the mean and the variance of X respectively. Then match List-I with List-II

List-I	List-II
(A) If Var (X) = $a$ , then Var (2X + 3) is	(I) 11 $a$
(B) If E (X) = $a$ , then E (2X) is	(II) 6 $a$
(C) If Var (X) = $a$ , then Var(3X - $a$ ) + Var ( $\sqrt{2}x + \beta$ ) is	(III) 4 $a$
(D) If E (X) = $\frac{5a}{12}$ , then E (12X + $a$ ) is	(IV) 2 $a$

Choose the correct answer from the options given below:

2025: 30 May Shift 2

A random variable X has the following probability distribution:

X	0	1	2	3
P(X)	0.2	0.1	0.3	0.4

The variance of X will be

A die is rolled thrice. What is the probability of getting a number greater than 444 in the first and the second throw of dice and a number less than 444 in the third throw ?

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

A die is rolled thrice. What is the probability of getting a number greater than $4$ in the first and the second throw of dice and a number less than $4$ in the third throw ?