Correct Answer -
1
2
Let A, B, C be the events of solving the problem by the 1st, 2nd and 3rd student respectively. Then,
P(A)=
1
4
,P(B)=
1
5
and P(C)=
1
6
⇒P(
ˉ
A
)=(1-
1
4
)=
3
4
,P(
ˉ
B
)=(1-
1
5
)=
4
5
and P(
ˉ
C
)=(1-
1
6
)=
5
6
.
∴ P(none solves the problem)= P [(not A) and (nor B)and (ot C)]
=P(
ˉ
A
and
ˉ
B
and
ˉ
C
)=P(
ˉ
A
)×P(
ˉ
B
)×P(
ˉ
C
).
