Question

Two unbiased coins are tossed simultaneously. Find the probability of getting
$i.$ two heads
$ii.$ one tail
$iii.$ at least one tail
$iv.$ at most one tail
$v.$ no tail

Answer 1

If two unbiased coins are tossed simultaneously, then the total outcomes may be $HH,HT,TH,TT$.

No. of total outcomes = $4$

$\left(i\right)$ two heads

favourable outcome for two heads are $HH$.

No. of favourable outcomes = $1$

$P\left(\text{two heads}\right)=\frac{1}{4}$

$\left(ii\right)$ favourable outcome for one tail are $TH,HT$.

No. of favourable outcomes = $2$

$P\left(\text{one tail}\right)=\frac{2}{4}=\frac{1}{2}$

$\left(iii\right)$ favourable outcome for at least one tail are are $TH,HT,TT$.

No. of favourable outcomes = $3$

$P\left(\text{at least one tail}\right)=\frac{3}{4}$

$\left(iv\right)$ favourable outcome for at least one head are are $TH,HT,HH$.

No. of favourable outcomes = $3$

$P\left(\text{at least one head}\right)=\frac{3}{4}$

$\left(v\right)$ favourable outcome for no tail are $HH$.

No. of favourable outcomes = $1$

$P\left(\text{no tail}\right)=\frac{1}{4}$