Find the probability distribution of the number of tails in the simultaneous tosses of three coins.

(N/A) When three coins are tossed simultaneously,the sample space is $S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$.
Let $X$ represent the number of tails.
It can be seen that $X$ can take the values $0, 1, 2,$ or $3$.
$P(X=0) = P(HHH) = \frac{1}{8}$
$P(X=1) = P(HHT) + P(HTH) + P(THH) = \frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8}$
$P(X=2) = P(HTT) + P(THT) + P(TTH) = \frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8}$
$P(X=3) = P(TTT) = \frac{1}{8}$
Thus,the probability distribution is as follows:

$X$	$0$	$1$	$2$	$3$
$P(X)$	$\frac{1}{8}$	$\frac{3}{8}$	$\frac{3}{8}$	$\frac{1}{8}$