Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

Statement-1: The probability of drawing either a king or an ace from a pack of 52 playing cards is 2/13.

Statement-2: For any two events A and B, 

$P(A ∪ B) = P(A) +P(B) - P(A ∩ B)$

Options:

Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for Statement 1.

Statement 1 is True, Statement 2 is False.

Statement 1 is False, Statement 2 is True.

Correct Answer:

Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

Explanation:

Clearly, statement-2 is true (see theory).

Consider the following events.

A =Getting a king in a draw, B-Getting an ace in a draw

Clearly, $P(A)=\frac{1}{13}, P(B)=\frac{1}{13}, P(A ∩ B) = 0 $

Required probability $= P(A ∪ B)$

$=P(A)+P(B)-P(A ∩ B)=\frac{1}{13}+\frac{1}{13}=\frac{2}{13}$