There are three bags. The first bag contains 3 white balls, 2 red balls and 4 black
balls, the bag contains 2 white, 3 red and 5 black balls and the third bag contains 3
white, 4 red and 2 black balls. One bag is chosen at random and a ball is drawn. The
drawn ball happens to be a red. What is the probability that the red ball drawn was
taken from (1) first bag, (2) second bag and (3) third bag?
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Step-by-step explanation:
The event of selecting a red ball is denoted by 'R'.
The event of selecting the bag A is denoted by 'A'.
The event of selecting the bag B is denoted by 'B'.
Bag-A has 2 white and 3 red balls
Bag-B has 4 white and 5 red balls
P(A)=P(B)=
2
1
,P(
A
R
)=
5
3
,P(
B
R
)=
9
5
From Bayes' theorem,we get
P(
R
B
)=
P(R)
P(
B
R
)P(B)
=
P(
A
R
)P(A)+P(
B
R
)P(B)
P(
B
R
)P(B)
=
(
5
3
)(
2
1
)+(
9
5
)(
2
1
)
(
9
5
)(
2
1
)
=
52
25
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