An urn contains 4 blue and 3 green balls. A ball is drawn at random from the
urn, its colour is noted and kept aside. Two balls of opposite colour are added
to the urn. A ball is then drawn from the urn, find the probability that the ball
is green.
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Answer:
The urn contains 5 red and 5 black balls.
Let a red ball be drawn in the first attempt.
∴P(drawing a red ball)=
10
5
=
2
1
If two red balls are added to the urn, then the urn contains 7 red and 5 black balls.
P( drawing a red ball)=
12
7
Let a black ball be drawn in the first attempt.
∴P(drawing a black ball in the first attempt)=
10
5
=
2
1
If two black balls are added to the urn, then the urn contains 5 red and 7 black balls.
P(drawing a red ball)=
12
5
Therefore, probability of drawing second ball as red is
2
1
×
12
7
+
2
1
×
12
5
=
2
1
(
12
7
+
12
5
)=
2
1
×1=
2
1
=0.5
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