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(A) The sample space $S$ for tossing three fair coins is given by: $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$. The total number of outcomes is $

Vedclass · Accepted Answer

$\frac{3}{8}$

Vedclass · Answer

(A) The sample space $S$ for tossing three fair coins is given by: $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$. The total number of outcomes is $n(S) = 8$. $X$ is a random variable representing the number of heads. We need to find $P(X = 2)$,which is the probability of getting exactly two heads. The outcomes with exactly two heads are $\{HHT, HTH, THH\}$. Thus,the number of favorable outcomes is $n(X = 2) = 3$. Therefore,$P(X = 2) = \frac{n(X = 2)}{n(S)} = \frac{3}{8}$.

$x$	$0$	$1$	$2$	$3$
$P(x)$	$0.2$	$k$	$k$	$2k$

Let $X$ be a random variable representing the number of heads obtained when three fair coins are tossed simultaneously. Find the value of $P(X = 2)$.

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