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JEE Advanced 2019 Paper 1
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© examsnet.com
Question : 45
Total: 54
There are bags
B
1
,
B
2
and
B
1
contains 5 red and 5 green balls,
B
2
contains 3 red 5 green balls, and
B
3
contains 5 red and 3 green balls, Bags
B
1
,
B
2
and
B
3
have probabilities
3
10
,
3
10
and
4
10
respectively of being chosen. A bag is selected at randomand a balls is chosen at random from the bag. Then which of the following options is/are correct?
Probability that the chosen balls is green equals
39
80
Probability that the selected bag is
B
3
, given that the chosen ball is green, equals
5
13
Probability that the chosen ball is green, given that the selected bag is
B
3
,equals
3
8
Probability that the selected bag is
B
3
and the chosen ball is green equals
3
10
Validate
Solution:
B
i
= Event for choosing bag
B
i
=
i
=
1
,
2
,
3
.
G = Event for choosing a green ball
P
(
G
)
=
P
(
B
1
)
P
(
G
B
1
)
+
P
(
B
2
)
P
(
G
B
2
)
+
P
(
B
3
)
P
(
G
B
3
)
=
3
10
×
5
10
+
3
10
×
5
8
+
4
10
×
3
8
=
3
20
+
3
16
+
3
20
=
39
80
Option 1 correct
P
(
B
3
G
)
=
P
(
B
3
∩
G
)
P
(
G
)
=
4
10
×
3
8
39
80
=
4
13
option 2 incorrect
P
(
G
B
3
)
=
3
8
option 3 is correct
P
(
B
3
∩
G
)
=
P
(
B
3
)
⋅
P
(
G
B
3
)
=
4
10
×
3
8
=
3
20
option 4 incorrect
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