In tossing three coins, the sample space is given gy
S={HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.
And, therefore, n(S) = 8.
(i) Let E1 = event of getting all heads. Then,
E1={HHH} and, therefore, n(E1)=1.
∴ P (getting all heads) =P(E1)=
n(E1)
n(S)
=
1
8
.
(ii) Let E2 = event of getting 2 heads. Then,
E2={HHT,HTH,THH} and, therefore, n(E2)=3.
∴ P (getting 2 heads) =P(E2)=
n(E2)
n(S)
=
3
8
.
(iii) Let E3 = event of getting 1 head. Then,
E3={HTT, THT, TTH} and, therefore, n(E3)=3.
∴ P (getting 1 head) =P(E3)=
n(E3)
n(S)
=
3
8
.
(iv) Let E4 = event of getting at least 1 heads. Then,
E4={HTT, THT, TTH, HHT, HTH, THH, HHH} and, therefore, n(E4)=7.
∴ P (getting at least 1 head) =P(E4)=
n(E4)
n(S)
=
7
8
.
(v) Let E5 = event of getting at least 2 heads. Then,
E5={HHT, HTH, THH, HHH} and, therefore, n(E1)=1.
∴ P (getting all heads) =P(E5)=
n(E5)
n(S)
=
4
8
=
1
2
.
