Probability (tossing coin)

2. Example-3:
Three coins are tossed, find the probability of getting:
(i) One head
(ii) Exactly two heads
(iii) No head
(iv) At most one head
(v) At least one head
Solution:
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
n (S) = 8
(i) Let A = One head
A = {HTT, THT, TTH}
n (A) = 3
(ii) Let B = exactly two heads
B = {HHT, HTH, THH}
n (B) = 3
(iii) Let C = no head
( ) ( )
( )
375.0
8
3
Sn
An
AP ===
( ) ( )
( )
375.0
8
3
Sn
Bn
BP ===

3. C = {TTT}
n (C) = 1
(iv) Let D = at most one head
D = {HTT, THT, TTH, TTT}
n (D) = 4
(v) Let E = at least one head
E = {HHH, HHT, HTH, HTT, THH, THT, TTH}
n (E) = 7
( ) ( )
( )
125.0
8
1
Sn
Cn
CP ===
( ) ( )
( )
5.0
8
4
Sn
Dn
DP ===
( ) ( )
( )
875.0
8
7
Sn
En
EP ===