Markov Chains and absorption probabilites

[macca1994]

Homework Statement

Could someone please help me with this question?

A single-celled organism contains N particles, some of which are of type A, the others of
type B . The cell is said to be in state i , where 0<=i<=N if it contains exactly i particles
of type A. Daughter cells are formed by cell division, but first each particle replicates itself;
the daughter cell inherits N particles chosen at random from the 2i particles of type A
and 2N-2i of type B in the parent cell.

Find the absorption probabilities and expected times to absorption for the case N = 3.

Homework Equations

The Attempt at a Solution

So far i have that the absorbing states are i=0 and i=3 but can't work out the probabilities or times to absorption. Don't know where to start now that i have my absorbing states

 

[Ray Vickson]

From state i, the (A,B) numbers of the daughter are determined by N independent "draws", with probabilities P(A) = i/N and P(B) = 1-P(A) in each draw.

 

[macca1994]

So is the probability of say reaching state 1 from state 2 1/5 from the number of possible combinations of the daughter cell or am i going about this the wrong way?

 

[Ray Vickson]

So is the probability of say reaching state 1 from state 2 1/5 from the number of possible combinations of the daughter cell or am i going about this the wrong way?

I have said all I intend to say on the subject.