Bag A=(4R+5B) balls

⇒ Bag B=(3R+6B) balls

⇒ Probability of red form bag A and black from bag B =

9

4

×

10

6

=

90

24

⇒ Probability of red from bag B and black from bag A =

10

3

×

9

5

=

90

15

⇒ P(balls of different colours)=P( red from bag A and black from bag B)+P( red from bag B and black from bag A)

=

90

26

+

90

15

=

90

41

All the best student,

Hope this helps you.