Question:
A coin is tossed 3 times. List the possible outcomes. Find the probability of getting
(i) all heads
(ii) atleast 2 heads
Solution:
The possible outcomes if a coin is tossed 3 times is
S = {(HHH), (TTT), (HTT), (THT), (TEH), (THH), (HTH), (HHT)}
(i) Let $E_{1}=$ Event of getting all heads $=\{(H H H)\}$
$\therefore \quad n\left(E_{1}\right)=1$
$\therefore \quad P\left(E_{1}\right)=\frac{n\left(E_{1}\right)}{n(S)}=\frac{1}{8}$
(ii) Let $E_{2}=$ Event of getting atleast 2 heads $=\{(H H T),(H T H),(T H H),(H H H)\}$
$\therefore \quad n\left(E_{2}\right)=4$
$\therefore$ $P\left(E_{2}\right)=\frac{n\left(E_{2}\right)}{n(S)}=\frac{4}{8}=\frac{1}{2}$