Let
E be the event ‘at least two heads appear’ and  F be the event ‘first coin shows tail’ Then
E = {HHH, HHT, HTH, THH}
and
F = {THH, THT, TTH, TTT}
Therefore
P(E) = P ({HHH}) + P ({HHT}) + P ({HTH}) + P ({THH})
= 1
1
1
1
1
8
8
8
8
2
+
+
+
=
 (Why )
and
P(F) = P ({THH}) + P ({THT}) + P ({TTH}) + P ({TTT})
= 1
1
1
1
1
8
8
8
8
2
+
+
+
=
Also
E ∩ F = {THH}
with
P(E ∩ F) = P({THH}) = 1
8
Now, suppose we are given that the first coin shows tail, i e