DSE 2016 doubt

[AP199]

Can anyone help with this?

[Gin_no]

Que. 6


position at t=10 (A, C)

Ans. (1/2, 0, 1/2,0)

Am I right ?

[Gin_no]

Que.7



Ans. (1/2)^5

[Econenthusiast]

Gin_no I've a doubt here though, in order to find the final probability at t= 10, shouldn't we make use of conditional probability ?

[Gin_no]

why and how conditional probability ? This is clear  that at = 1,3,5..his position is B,D with prob. 1/2 each and at t=2,4,6.. his position is A,C with prob. 1/2 each.  

[Econenthusiast]

okay, I thought that the probability of being at B or D is conditional upon the probability of being at A.

[Gin_no]

May be I am wrong.  We should confirm it from others too.

[Nikkita]

It's right..
Even if we try to use conditional probability, we can, but all extra terms will get cancel out because of independent sort of nature..

[AP199]

Thanks