CUET Mathematics 2024 - Let X denote the number of hours you play during a randomly selected day. The probability that X can take values x has the following form, where c is some constant. P(X=x)=\arraylll 0.1, & if x=0 \\ cx, & if x=1 or x=2 \\ c(5-x), & if x=3 or x=4 \\ 0, & otherwise array. Match List-I with List-II : | PYQs + Solutions

CUET Mathematics 2024

Algebra

Probability

Easy

Let $X$ denote the number of hours you play during a randomly selected day. The probability that $X$ can take values $x$ has the following form, where $c$ is some constant.
$\mathrm{P}(\mathrm{X}=\mathrm{x})=\left\{\begin{array}{lll} 0.1, & \text { if } \mathrm{x}=0 \\ \mathrm{cx}, & \text { if } \mathrm{x}=1 \text { or } \mathrm{x}=2 \\ \mathrm{c}(5-\mathrm{x}), & \text { if } \mathrm{x}=3 \text { or } \mathrm{x}=4 \\ 0, & \text { otherwise } \end{array}\right.$
Match List-I with List-II :

List-I List-II

(A) $c$ (I) 0.75

(B) $P(X \leq 2)$ (II) 0.3

(C) $P(X = 2)$ (III) 0.55

(D) $P(X \geq 2)$ (IV) 0.15

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (I), (B) - (II), (C) - (IV), (D) - (III)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

✅ Correct Option: 2

Let's find the value of constant

c

Since this is a probability distribution, the sum of all probabilities must equal 1.

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

0.1 + c(1) + c(2) + c(5-3) + c(5-4) = 1

0.1 + c + 2c + 2c + c = 1

0.1 + 6c = 1

6c = 0.9

c = 0.15

Now let's calculate each probability:

P(X = 0) = 0.1

P(X = 1) = c(1) = 0.15

P(X = 2) = c(2) = 0.3

P(X = 3) = c(5-3) = 0.3

P(X = 4) = c(5-4) = 0.15

Let's find the requested probabilities:

(A)

c = 0.15

(B)

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1 + 0.15 + 0.3 = 0.55

(C)

P(X = 2) = 0.3

(D)

P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.3 + 0.3 + 0.15 = 0.75

Therefore, the matching is:

(A)

c

→ (IV) 0.15

(B)

P(X \leq 2)

→ (III) 0.55

(C)

P(X = 2)

→ (II) 0.3

(D)

P(X \geq 2)

→ (I) 0.75

Related questions:

CUET Mathematics 2024

X

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

CUET Mathematics 2024

4

4

CUET Mathematics 2024