Algebra

Probability

Medium

core

A random variable X has the following probability distribution

X 0 1 2 3 4 5
P(X) 0.1 k 0.2 2k 0.3 k

Then P (X < 3) is

X	0	1	2	3	4	5
P(X)	0.1	k	0.2	2k	0.3	k

0.1

0.2

0.3

0.4

✅ Correct Option: 4

A probability distribution table is given with some known values and some unknown values in terms of $k$ .

In any probability distribution, all probabilities must add up to $1$ .

Adding all the probabilities and setting them equal to 1:

$P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) = 1$

$0.1 + k + 0.2 + 2k + 0.3 + k = 1$

$0.6 + 4k = 1$

$4k = 0.4$

$k = 0.1$

$P(X < 3)$ means the probability that $X$ is less than 3.

This includes $X = 0, 1, 2$ (not 3).

$P(X < 3) = P(X=0) + P(X=1) + P(X=2)$

$P(X < 3) = 0.1 + k + 0.2$

$P(X < 3) = 0.1 + 0.1 + 0.2$

$P(X < 3) = 0.4$

Therefore, $P(X < 3) = 0.4$

2026: 31 May Shift 2

Let X denote the number of hours a person watches television during a randomly selected day. The probability that X can take the value $x_i$ , has the following form, where $k$ is some unknown constant.

$P(X=x_i) = \begin{cases} 0.5 & \text{if } x_i=0 \\ kx_i & \text{if } x_i=1 \\ k(4-x_i) & \text{if } x_i=2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$

The probability that the person watches at most 2 hours of television on a selected day is :

2026: 21 May Shift 2

Let A and B be two events such that $P(A \cap B) = 0$ then $P(A|(A \cup B))$ is equal to:

2026: 25 May Shift 1

A four digit number is formed by using the digits 1, 2, 4 and 5 with no repetition. The probability that the number is divisible by 5, is

2026: 26 May Shift 2

Bag I contains 3 red and 4 black balls while Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. then the probability that it was drawn from Bag I is

2025: 15 May Shift 2

A player participates in 3 matches against three teams T₁, T₂ and T₃.The probability of winning a match against teams T₁, T₂ and T₃ are 0.2, 0.3 and 0.9 respectively. If 'wins' can be regarded as independent events, then the probability that he

(A) wins all the 3 matches is 0.054

(B) wins no match is 0.054

(D) wins exactly one match is 0.542

Choose the correct answer from the options given below:

2023: 30 May Shift 3

The mean number of heads in two tosses of a coin is :

A random variable X has the following probability distribution X012345P(X)0.1k0.22k0.3k Then P (X < 3) is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

A random variable X has the following probability distribution

X 0 1 2 3 4 5
P(X) 0.1 k 0.2 2k 0.3 k

Then P (X < 3) is