Question

A coin is tossed three times. Then find the probability of the following events.
(1) getting tail in the middle toss; and
(2) getting all heads.

Answer 1

Three coins tossed.
$\therefore$ The sample space is
$S=\{HHH,HHT,HTH,THH,HTT,THT,TTH,TTT\}$
$\therefore n\left(S\right)=8$
(1) Let $A$ be event of getting tail in middle toss.
$\therefore A=\{HTH,HTT,TTH,TTT\}$
$\therefore n\left(A\right)=4$
$\therefore P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{4}{8}=\frac{1}{2}$
(2) Let $B$ be the event of getting all heads.
$\therefore B=\left\{HHH\right\}$
$\therefore n\left(B\right)=1$
$\therefore \left(PB\right)=\frac{n\left(B\right)}{n\left(S\right)}$
$=\frac{1}{8}$