A bag contain 2 white balls, 3 black balls and 4 red balls. A ball is drawn at random from the bag. The probability that the ball drawn will be black is:
4/9
2/9
0
1/3
Answers
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0
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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