Consider the event E ‘three heads
or three tails’, F ‘at least two heads’ and G ‘at most two heads’ Of the pairs (E,F),
(E,G) and (F,G), which are independent which are dependent Solution The sample space of the experiment is given by
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Clearly
E = {HHH, TTT}, F= {HHH, HHT, HTH, THH}
© NCERT
not to be republished
PROBABILITY      545
and
G = {HHT, HTH, THH, HTT, THT, TTH, TTT}
Also
E ∩ F = {HHH}, E ∩ G = {TTT}, F ∩ G = { HHT, HTH, THH}
Therefore
P(E) = 2
1
4
1
7
, P(F)
, P(G)
8
4
8
2
8
=
=
=
=
and
P(E∩F) = 1
1
3
, P(E
G)
, P(F
G)
8
8
8
∩
=
∩
=
Also
P(E)