Confusion in without/ with replacement questions

[user3968]

Can someone explain why did Greg said the probability that a blue one is drawn first is 2/3 (written in red)

Also will it always be the case that with and without replacement will have the same probability of the drawing out of the marble irrespective its drawn, first , second or third?

[cylverixxx]

@user3968

Also will it always be the case that with and without replacement will have the same probability of the drawing out of the marble irrespective its drawn, first , second or third?

It’s a combinatorics exercise where you have to count how many arrangements in:

(R,B,R,R,B,B,B,B,G,G,G)

have blue in the third position. Noting the bijection already tells you that exactly \frac 4{10} = \frac 25 of the total arrangements have blue marbles in the third position so yeah…