Statement A (Assertion): Cards numbered 5 to 102 are placed in a … - Vidyadip

MCQ

Statement A (Assertion): Cards numbered 5 to 102 are placed in a box. If a card is selected at random from the box, then the probability that the card selected has a number which is a perfect square, is $\frac{4}{49}$.
Statement R (Reason) : Probability of an event $E$ is a number such that $0 \leq P(E) \leq 1$.

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.
Total number of cards $=102-5+1=98$
So, total number of possible outcomes $=98$
Let $E$ be the event of selecting a card with perfect square number on it.
So, favourable outcomes to $E$ are $\{9,16,25,36,49,64$, $81,100\}$ i.e., 8 $ \therefore \quad P(E)=\frac{8}{98}=\frac{4}{49} $
So, Assertion and Reason both are true but Reason is not the correct explanation of Assertion.

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