probablity question

Here we need to notice that in the question the probability of the ball transferred from bag A to B is being asked not the probability of getting a red ball finally.

So, we need to find the probability of transferring a black ball from bag A to B (in other words we can say we need to find the probabilty of getting a black ball from bag A)

The Probability of transferring a black ball from bag A is = 4/7 (no. of favourable outcomes / total outcomes)