1. (2 pts) There are 6 black chips and 8 red chips in a bag. Suppose you take one chip randomly from the bag, and it is red. You do not put the red chip back to the bag (i.e., no replacement); and take a chip randomly from the chips remaining in the bag.

What is the probability that the second pick is again a red chip? (keep 4 digits after decimal point)

1. There are 6 black chips and 8 red chips in a bag. Suppose you take one chip randomly from the bag, and it is red. You do not put the red chip back to the bag (i.e., no replacement); and take a chip randomly from the chips remaining in the bag.

(1a)What is the probability that the second pick is again a red chip? (keep 4 digits after decimal point)

2. A jar contains 5 green chips, 7 white chips, and 8 red chips. A chip is drawn and replaced back to the jar, and then the second chip is drawn.

(2.a) What is the probability that the first draw is a green one?

(2.b) What is the probability that a white chip on the second draw, given that a green chip was drawn on the first? (Keep 4 digits after decimal point.)

(2.c) What is the probability that two draws are both red? (Keep 4 digits after decimal point.) (Show your calculations. 1 point for the result, 1 point for the calculations.)

(2.d) What is the probability that "a green chip on the first draw and a white chip on the second draw"? (Keep 4 digits after decimal point.) (Show your calculations. 1 point for the result, 1 point for the calculations.)

(2.e) What is the probability that the result of two draws contains one red and one green, regardless of the order drawn? (Keep 4 digits after decimal point.) (Show your calculations. 1 point for the result, 1 point for the calculations.)

(2.f)What is the probability that two draws have different colors? (Keep 4 digits after decimal point.) (Show your calculation steps. No credits if no calculations.)

3. A machine is composed of three independent components, A, B, and C. The probability for component A to work normally is 0.7. The probability for component B to work normally is 0.8. The probability for C to work normally is 0.9. Calculate the following probabilities.

(3.a) What is the probability that component C does not work normally? (show calculations)

(3.b) What is the probability that component B works normally, given that component A does not work normally? (show calculations)

3.c) What is the probability that all the three components work normally? (Keep 4 digits after decimal point.) (Show calculations.)

(3d)What is the probability that all the three components break down at same time? (Keep 4 digits after decimal point.) (show calculations. No credits if no calculations.)