The probability distribution of a random variable X is given by, X, 0, 1, 2, P(X), k, 2k, 3k, If k > 0, then P(0 < X ≤ 2) is equal to Option 1: 1/6 Option 2: 5/6 Option 3: 7/8 Option 4: 9/16

Answer: 5/6. Solution: The probability distribution of a random variable X is given by:, X, 0, 1, 2, P(X), k, 2k, 3k, In any probability distribution, all probabilities must sum to 1. P(X=0) + P(X=1) + P(X=2) = 1 k + 2k + 3k = 1 6k = 1 k = 1/6 The expression P(0 < X ≤ 2) represents the probability that X is greater than 0 and less than or equal to 2. From the table, this includes X = 1 and X = 2, but excludes X = 0. P(0 < X ≤ 2) = P(X=1) + P(X=2) P(0 < X ≤ 2) = 2k + 3k P(0 < X ≤ 2) = 5k P(0 < X ≤ 2) = 5 x 1/6 P(0 < X ≤ 2) = 5/6

Algebra

Probability

Medium

common

The probability distribution of a random variable X is given by

X 0 1 2
P(X) k 2k 3k

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

$\frac{1}{6}$

$\frac{5}{6}$

$\frac{7}{8}$

$\frac{9}{16}$

✅ Correct Option: 2

The probability distribution of a random variable X is given by:

X	0	1	2
P(X)	k	2k	3k

In any probability distribution, all probabilities must sum to 1.

$P(X=0) + P(X=1) + P(X=2) = 1$

$k + 2k + 3k = 1$

$6k = 1$

$k = \frac{1}{6}$

The expression $P(0 < X \leq 2)$ represents the probability that X is greater than 0 and less than or equal to 2.

From the table, this includes X = 1 and X = 2, but excludes X = 0.

$P(0 < X \leq 2) = P(X=1) + P(X=2)$

$P(0 < X \leq 2) = 2k + 3k$

$P(0 < X \leq 2) = 5k$

$P(0 < X \leq 2) = 5 \times \frac{1}{6}$

$P(0 < X \leq 2) = \frac{5}{6}$

2025: 30 May Shift 1

A bag contains 6 red balls, 4 green balls and 10 blue balls. Three balls are drawn with replacement. The probability of getting at least 1 green ball is:

2026: 30 May Shift 1

If E and F are two events such that P(E) = 0.8, P(F) = 0.7 and P(E ∩ F) = 0.6 then $P(\bar{E}/\bar{F})$ is:

2025: 14 May Shift 1

What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on 1 face?

2026: 31 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	If $A$ and $B$ are mutually exclusive events then $P(A \cup B) =$	I.	$\dfrac{P(A \cap B)}{P(B)}, P(B) \neq 0$
B.	If $A$ and $B$ are independent events then $P(A \cap B) =$	II.	$\dfrac{P(A \cap B)}{P(A)}, P(A) \neq 0$
C.	If $A$ and $B$ are two events of a sample space of an experiment, then $P(A/B) =$	III.	$P(A) \cdot P(B)$
D.	If $A$ and $B$ are two events of a sample space of an experiment, then $P(B/A) =$	IV.	$P(A) + P(B)$

Choose the correct answer from the options given below:

2022: 7 Aug Shift 2

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 will not germinate, given that the seed is of type $A_3$ .

2022: 16 July Shift 2

Let X be the random variable with probability distribution given by the following table.

X	0	1	2	3
P(X = x)	$\frac{1}{8}$	k	$\frac{3}{8}$	$\frac{1}{8}$

The value of $P(X \leq 1)$ is:

The probability distribution of a random variable X is given by X012P(X)k2k3k If k > 0, then P(0<X≤2)P(0 < X \leq 2)P(0<X≤2) is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The probability distribution of a random variable X is given by

X 0 1 2
P(X) k 2k 3k

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