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Probability — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsProbability1 Mark
MCQ
Statement A (Assertion) : A number is selected from the numbers 1 to 20 . The probability that it will be a prime is $\frac{2}{5}$.
Reason (R) : There exists 25 prime numbers from natural number 1 to 100 .
  • A
    Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
  • ✓
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
  • C
    Assertion $(A)$ is true but reason $(R)$ is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.
✓

Answer

Correct option: B.
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
(b):Clearly, Reason is true.
Now, total number of outcomes $=20$
Favourable outcomes are $\{2,3,5,7,11,13,17,19\}$ i.e., 8 in number.
$\therefore \quad$ Required probability $=\frac{8}{20}=\frac{2}{5}$
$\therefore \quad$ Assertion and Reason both are true but Reason is not the correct explanation of Assertion.

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