Question

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

Answer 1

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