Question:
Two coins are tossed once, where
(i) E: tail appears on one coin, F: one coin shows head
(ii) E: not tail appears, F: no head appears
Solution:
If two coins are tossed once, then the sample space S is
S = {HH, HT, TH, TT}
(i) E = {HT, TH}
F = {HT, TH}
$\therefore \mathrm{E} \cap \mathrm{F}=\{\mathrm{HT}, \mathrm{TH}\}$
$\mathrm{P}(\mathrm{F})=\frac{2}{8}=\frac{1}{4}$
$\mathrm{P}(\mathrm{E} \cap \mathrm{F})=\frac{2}{8}=\frac{1}{4}$
$\therefore P(E \mid F)=\frac{P(E \cap F)}{P(F)}=\frac{2}{2}=1$
(ii) E = {HH}
F = {TT}
$\therefore \mathrm{E} \cap \mathrm{F}=\Phi$
P (F) = 1 and P (E ∩ F) = 0
$\therefore \mathrm{P}(\mathrm{E} \mid \mathrm{F})=\frac{\mathrm{P}(\mathrm{E} \cap \mathrm{F})}{\mathrm{P}(\mathrm{F})}=\frac{0}{1}=0$