You are sent to prison though quite innocent! After a few years, the king decides to play a "life or death" game with you.

He gives you 20 blue marbles, 20 red marbles, and two cloth bags. You are allowed to fill the bags with the 40 marbles as you wish. The king will then choose a bag first and then a marble from that bag. If the marble he chooses is blue, you are set free! If the marble is red (or there are no marbles in the bag), you are executed.

(1) You decide to place 10 red marbles and 10 blue marbles in

each bag. Find the probability that the king will set you free using a tree diagram.

(2) If you decide to place 20 red marbles in one bag and 20 blue

marbles in the other bag, has your probability of freedom increased, decreased, or remained the same? Explain why.

(3) If you decide to put 5 blue marbles and 1 red marble in one

bag and the rest of the marbles in the other bag, what is your probability of freedom? Give an exact fractional answer and an approximate answer rounded to the nearest percent.

(4) There is a better strategy than these three options. What

strategy would give you the greatest chance for freedom?