1. A container has 1 white marble, 3 red marbles, and 2 blue marbles. A marble is selected at random from the container. If the marble is white: we toss it away, select another marble from the container and record the outcome. If the marble is red: a fair coin is tossed and the outcome recorded (Heads or Tails). If the marble is blue: we take all the blue marbles out of the container, and THEN select another marble from the container and record the outcome. So - the outcomes are either two colors, or a color followed by H (head) or T (tail). (a) Make a tree diagram of this experiement. label all the branches with their probabilities! (b) List the sample space of all possible outcomes! (c) What is the probability that the first marble is red? (d) What is the probability that the second marble is red if we KNOW that the first marble was white? (e) What is the probability that an outcome describes the coin as landing Heads? (f) What is the probability that the second marble is red? (g) What is the probability that the first marble was blue if we KNOW that the second marble is red? . Jansen Electronics has four machines that produce identical components for use in its DVD players. The proportion of the components produced by each machine and the probability of a component produced by that machine being defective are shown in the accompanying table. Proportion of Probabilty of Machine components produced defective component 0.50 0.10 II 0.30 0.05 III 0.20 0.01 (a) What is the probability that a component selected at random is defective? (b) What is the probability that a component selected at random was produced by Machine I, given that it is defective