Suppose three coins are tossed simultaneously. If X denotes the number of heads, then probability…
Suppose three coins are tossed simultaneously. If X denotes the number of heads, then probability distribution of X is
Solution
Let X denotes the number of heads. Thus, the possible values of X are $0,1,2$ and 3 .
$\begin{aligned}
\mathrm{P}(\mathrm{X}=0) & =\mathrm{P}(\text { getting no head }) \\
& =\mathrm{P}(\mathrm{TTT})=\frac{1}{8}
\end{aligned}$
$\begin{aligned}
\mathrm{P}(\mathrm{X}=1) & =\mathrm{P}(\text { getting one head }) \\
& =\mathrm{P}(\text { HTT, THT }, \mathrm{TTH})=\frac{3}{8} \\
\mathrm{P}(\mathrm{X}=2) & =\mathrm{P}(\text { getting two heads }) \\
& =\mathrm{P}(\text { HHT }, \text { THH, HTH })=\frac{3}{8} \\
\mathrm{P}(\mathrm{X}=3) & =\mathrm{P}(\text { getting three heads }) \\
& =\mathrm{P}(\text { HHH })=\frac{1}{8}
\end{aligned}$
$\therefore \quad$ Option (B) is the correct answer.
