This document provides the probability of different outcomes when three coins are tossed. It defines the sample space as all possible combinations of heads and tails across three coins. It then calculates the probability of (i) getting one head, (ii) getting exactly two heads, (iii) getting no heads, (iv) getting at most one head, and (v) getting at least one head by defining the event space for each and dividing its size by the total sample space size.

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 ===