Box I contains 4 red and 8 blue marbles while box II contains 5 red and 3 blue marbles. An unfair coin is tossed – whose probability of turning up heads is 40%. If the coin comes up heads box I is chosen and a random marble is chosen, otherwise if it is tails the marble is chosen from box II.
Suppose after the first marble is chosen – the experiment is repeated. Assume the first marble is NOT put back into its box. The coin is flipped again and another marble is chosen from either box I or box II.
(d) What is the probability that the second marble has the same color as the first marble?
I feel like the answer is so obvious, but I can't get it. In the first case $P(Red)$ = .5083 while $P(Blue)$ = 4917. I'm just confused after this point whether where I go after this.