In: Statistics and Probability
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.
What is the probability that the second marble has the same color as the first marble?