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.

Question

Mathematics

Viviana Macdonald

25 May, 15:56

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.

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Answers (1)

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Harper Vance · 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