Let X denotes the number of hours you st

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

Let X denotes the number of hours you study during a randomly selected school day. The random variable X has the following probability distribution.

X	0	1	2	3	4
P(X)	K	2K	2K	2K	K

Match List – I with List – II.

List - I	List - II
(A) Value of K	(I) $\frac{1}{4}$
(B) Probability you study at least two hours	(II) $\frac{1}{8}$
(C) Probability you study exactly two hours	(III) $\frac{3}{8}$
(D) Probability you study at most one hour	(IV) $\frac{5}{8}$

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (1) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

$∑P(X)=1⇒(k+2k+2k+2k+k)=1$

$⇒8k=1⇒k=\frac{1}{8}$

A. $k=\frac{1}{8}$ (II)

B. $P(X≥2)=5k=\frac{5}{8}$ (IV)

C. $P(X=2)=2k=\frac{1}{4}$ (I)

D. $P(X≤2)=3k=\frac{3}{8}$ (III)