Clearly, the sample space cosists of 1400 quations.
∴n(S)=1400
Let A= event of selecting an easy question, and
B= event of selecting a multiple - choice question.
Then, A∩B= event of selecting an easy multiple-choice question.
∴n(A)=(300+500)=800,n(B)=(500+400)=900
and n(A∩B)=500.
So, P(A)=
n(A)
n(S)
=
800
1400
=
4
7
,P(B)=
n(B)
n(S)
=
900
1400
=
9
14
and P(A∩B)=
n(A∩B)
n(s)
=
500
1400
=
5
14
Suppose b has already occurred and then A occurs.
Thus we have to find P(A/B).
Now, P(A/B)=
P(A∩B)
P(B)
=
(5/14)
(9/14)
=(
5
14
×
14
9
)=
5
9
.
Hence, the required probability is 5/9.
