Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

Statement-1: A natural number x is chosen at random from the first 100 natural numbers. The probability that $\frac{(x-10)(x-50)}{x-30}< 0$ is 0.28

Statement -2: For any event $A, 0 ≤ P(A)≤1$

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 not a correct explanation for Statement 1.

Explanation:

Clearly, statement-2 is true

Now, $\frac{(x-10)(x-50)}{x-30}< 0$

$⇔ 0 < x < 10 $ or $ 30 < x < 50$

$⇔ x=1, 2, 3, 4, 5, 6, 7, 8, 9 $ or $ x = 31, 32, ....49$

⇔ x takes 28 values

∴ Probability of given event $=\frac{28}{100}=0.28$