Statement A (Assertion): Three unbiased coins are tossed together… - Vidyadip

MCQ

Statement A (Assertion): Three unbiased coins are tossed together, then the probability of getting exactly 1 head is $\frac{3}{8}$.
Statement R (Reason) : Favourable number of outcomes do not lie in the sample space of total number of outcomes.

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):$\because$ Favourable outcomes always lies in the sample space of total number of outcomes. So, Reason is false.
Total possible outcomes are $1 HHH , HHT , HTH , THH$, TTH, THT, HTT, TTT] i.e., 8 in number. Let $E$ be the event of getting exactly 1 head.
$\therefore \quad$ Outcomes favourable to $E$ are $[T T H, T H T, H T T]$ i.e., 3 in number. $ \therefore \quad P(E)=\frac{3}{8} $
$\therefore \quad$ Assertion is true.

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