Question

Two coins are tossed once, where $E$ is the event of tail appearing on one coin, $F$ is the event of one coin shows head. Then the value of $P\left(E/F\right)$ is:

• A. $\frac{1}{3}$
• B. $1$
• C. $\frac{1}{4}$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $1$

The sample space of the given experiment is
$S=\{HH,HT,TH,TT\}$
Here, $E:$ tail appears on one coin
And $F:$ one coin shows head
$\Rightarrow E=\{HT,TH\}$ and $F=\{HT,TH\}$
$\Rightarrow E\cap F=\{HT,TH\}$
So, $P\left(E\right)=\frac{2}{4}=\frac{1}{2},P\left(F\right)=\frac{2}{4}=\frac{1}{2},P(E\cap F)=\frac{2}{4}=\frac{1}{2}$
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
$\Rightarrow P\left(E/F\right)=\frac{1/2}{1/2}=1$