Question

In tossing three coins together, what is the probability of getting i) at least one tail ii) at least one head ?

Answer 1

We have,

In tossing three coins, the sample space is given by,

$S=\{HHH,HHT,HTH,THH,HTT,THT,TTH,TTT\}$

Therefore,

$n\left(S\right)=8$

(1).Getting at least one tail. Then,

$E=\{HHT,HTH,THH,HTT,THT,TTH,TTT\}$

Therefore,

$n\left(E\right)=7$

Therefore, $\text{Probability}$$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{7}{8}$

(2).Getting at least one Head. Then,

$E=\{HHT,HTH,THH,HTT,THT,TTH\}$

Therefore,

$n\left(E\right)=7$

Therefore, $\text{Probability}$$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{7}{8}$

Hence, this is the answer.