Statement A (Assertion) : Two dice are rolled simultaneously. The… - Vidyadip

MCQ

Statement A (Assertion) : Two dice are rolled simultaneously. Then the probability of getting prime number on both dice is $\frac{1}{4}$.
Statement R (Reason) : Sum of probabilities of all the elementary events of an experiment is zero.

A
Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
✓
Assertion $(A)$ is true but reason $(R)$ is false.
D
Assertion (A) is false but reason $(R)$ is true.

✓

Answer

Correct option: C.

Assertion $(A)$ is true but reason $(R)$ is false.

(c):Clearly, Reason is false.
Now, total number of possible outcomes, when two dice are rolled simultaneously $=6 \times 6=36$
Favourable outcomes are $\{(2,2),(2,3),(2,5),(3,2)$, $(3,3),(3,5),(5,2),(5,3),(5,5)\}$ i.e., 9 in number.
$\therefore \quad$ Required probability $=\frac{9}{36}=\frac{1}{4}$
$\therefore \quad$ Assertion is true.

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