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