Question

Bag A has 4 blue and 5 red balls.
Bag B has 5 blue and 4 red balls.
I randomly choose a ball from bag A, then putting it into B. I then randomly choose a ball from bag B. What is the probability that the ball chosen from bag B is red?

Answer 1

is it (4/9*4/10 +5/9* 5/10 = 41/90)=41/90

Answer 2

Probability of having a fifth red ball in bag B is 5/9.
Probability that the ball chosen from bag B is red is:
\[\frac{1}{10}(4+\frac{5}{9})\]=41/90