Question

You have 9 pieces of wood of different lengths that you are attempting to glue together that will have a length of exactly 10 inches. The wood lengths are 1 inch, 2 inches, 3 inches, 4 inches, 5 inches, 6 inches, 7 inches, 8 inches, and 9 inches. What is the probability that you randomly choose one piece of wood keep it then randomly choose the second one to give you a total length of 10 inches.

Part 1:
Express the probability of the 1st chosen piece of wood.
Express the probability of the 2nd chosen piece of wood.

Part 2:
Explain how you arrived at the above probabilities.

Part 3:
Express your result in lowest terms.

Answer 1

Answer:

This is awfully simple. You have nine choices and eight of them are valid, so the odds of the first piece are 8/9. There is only one valid choice for the second, so the odds are 1/8. The odds of both choices being valid are 8/9 x 1/8 = 1/9.