A gambler has given you two jars and 20 marbles. Of these 20 marbles, 10 are red and 10 are green. You must put all 20 marbles in these two jars in such a way that each jar must have at least one marble in it. Then a friend of yours, who is blindfolded, will select one of the two jars at random and then will randomly select a marble from this jar. If the selected marble is red, you and your friend win $100.
a. If you put 5 red marbles and 5 green marbles in each jar, what is the probability that your friend selects a red marble?
b. If you put 2 red marbles and 2 green marbles in one jar and the remaining marbles in the other jar, what is the probability that your friend selects a red marble?
c. How should these 20 marbles be distributed among the two jars in order to give your friend the highest possible probability of selecting a red marble?