Question

Two coins are tossed once, where $E$ is the event of no tail appearing, $F$ is the event of no head appearing. Then the value of $P\left(E/F\right)$ is:

Answer 1

The sample space of the given experiment is
$S=\{HH,HT,TH,TT\}$
Here, $E:$ no tail appears
And $F:$ no head appears
$\Rightarrow E=\left\{HH\right\}$ and $F=\left\{TT\right\}$
$\Rightarrow E\cap F=\left\{\varphi \right\}$
So, $P\left(E\right)=\frac{1}{4},P\left(F\right)=\frac{1}{4},P(E\cap F)=\frac{0}{4}=0$
Now, we know that by definition of conditional probability,
$P\left(E/F\right)=\frac{P(E\cap F)}{P\left(F\right)}$
Substituting the values we get
$\Rightarrow P\left(E/F\right)=\frac{0}{1/4}=0$