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 straw 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. (*Hint* Make a list of the combinations that will add up to 10.) 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

The possible combinations are:
1,9
2,8
3,7
4,6
9,1
8,2
7,3
6,4

Total straws: 9
Probability of first being 1: 1/9
Probability of second being 9: 1/8
Probability of both: 1/9 x 1/8 = 1/72

This will be multiplied by 8 as there are 8 possible combinations:
8 x 1/72
= 8/72
= 1/9