Question

Three unbiased coins are tossed together . Find the probability of getting

$1.$ Two heads.

$2.$ At least two heads.

$3.$ No heads

Answer 1

When $3$ unbiased coins are tossed, the sample space is $\{HHH,HTH,HHT,THH,THT,TTH,HTT,TTT\}=8$

$1.$Event of getting two heads $=\{HTH,HHT,THH\}=3$

$P\left(TwoHeads\right)=\frac{3}{8}$

$2.$Event of getting At least two heads (two or more than $2$ heads) $=\{HHH,HTH,HHT,THH\}=4$

$P\left(AtleastTwoHeads\right)=\frac{4}{8}=\frac{1}{2}$

$3.$ Event of getting No heads $=\left\{TTT\right\}=1$

$P\left(NoHeads\right)=\frac{1}{8}$