maths helpp

hey, could anyone pls help me on the probabilities of this question I understand the values of n, but not the the mark scheme has written the probability values, thank you.

Two bags, A and B, each contain balls which are either red or yellow or green.
Bag A contains 4 red, 3 yellow and n green balls.
Bag B contains 5 red, 3 yellow and 1 green ball.
A ball is selected at random from bag A and placed into bag B.
A ball is then selected at random from bag B and placed into bag A.
The probability that bag A now contains an equal number of red, yellow and green balls
is p.
Given that p > 0, find the possible values of n and p.

So what have you (mark scheme) got for n and what do you think for the probbilities?

well the two values of n would be 2 and 5, and the probability would be 4/9x 3/9? for n=2
and for n=5 5/12x4/12 (what I thought)
I just dont rlly get the second probabilities?

For n=2, youve placed a red ball into bag B. Then what do you do?

you place a red ball into the bag B and take a green ball from bag B to put it in bag A

So what is the probability of choosing a green ball from bag B?

1/9

How many balls are in bag B (now, before you select the green)

ohh 10, because we've just put the red into the bag

Yes. Really its a conditional probability question so
p(red bag A AND green bag B) = p(green B | red A)*p(red A)
so make sure you model the "given" part correctly.

makes a lot of sense now, thanks.

Can you show how you would do this

What does it look like when you draw it? Show me please