Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Probability

Question:

A coin is tossed 3 times. If X denotes the number of heads, then Match List I with List II.

LIST I

LIST II

 A. P(X = 0)

 I. $\frac{1}{8}$

 B. P(X = 1)

 II. $\frac{7}{8}$

 C. P(X ≤ 2) 

 III. $\frac{4}{8}$

 D. P(X ≥ 2)

 IV. $\frac{3}{8}$ 

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

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

(A) $P(X = 0)={^3C}_0×(\frac{1}{2})^3=\frac{1}{8}$ (I)

(B) $P(X = 1)={^3C}_1×(\frac{1}{2})×(\frac{1}{2})^2=\frac{3}{8}$ (IV)

(C) $P(X ≤ 2)=1-P(X=3)$

$=1-{^3C}_3(\frac{1}{2})^3=\frac{7}{8}$ (II)

(D) $P(X ≥ 2)=P(X=2)+P(X=3)$

$={^3C}_2(\frac{1}{2})^3+{^3C}_3(\frac{1}{2})^3=\frac{4}{8}$ (III)