Question

Two coins are tossed once, where
(i) $E$ : tail appears on one coin, $F$ : one coin shows head
(ii) $E$ : no tail appears, $F$ : no head appears
Determine $P\left(E|F\right)$

• A. $1,0$
• B. $1,0.2$
• C. $0,2$
• D. $1,3$

Answer 1

Answer: (A)

$1,0$

If two coins are tossed once, then the sample space $S$ is

$S=\{HH,HT,TH,TT\}$

(i) $E=\{HT,TH\}$

$F=\{HT,TH\}$

$\therefore E\cap F=\{HT,TH\}$

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

$P(E\cap F)=\frac{2}{4}=\frac{1}{2}$

$\therefore P\left(E|F\right)=\frac{P(E\cap F)}{P\left(F\right)}=1$

(ii) $E=\left\{HH\right\}$

$F=\left\{TT\right\}$

$\therefore E\cap F=\Phi$

$P\left(F\right)=1$ and $P(E\cap F)=0$

$\therefore P\left(E|F\right)=\frac{P(E\cap F)}{P\left(F\right)}=\frac{0}{1}=0$