Suppose you have a reed of length 1 unit. If you haphazardly break this reed twice...

Suppose you have a reed of length 1 unit. If you haphazardly break this reed twice (forming 3 pieces), those 3 pieces might form a triangle, or they might not. What is the empirical probability that you can form a triangle from the pieces? Estimate this by “breaking” 2000 reeds twice and seeing if the parts form triangles.

Solutions

Expert Solution

Let's do the simulation in Excel:

The 1st cut is estimated by the RAND function. The 2nd cut is estimated by getting a random number between the 1st cut till its length.

Then the length of each cut is estimated. The conditions of the triangle are seen if they are satisfied are not. The conditions are that sum of two sides is greater than the third side. If all the conditions satisfy, a triangle can be formed. The output is:

We can see that 380 triangles have satisfied the conditions. Hence, the probability = 380/2000 = 0.19

Note: If you will perform the simulation at your own, the simularion will result into a slightly different probability. It will be closer than 0.20

orchestra answered 1 year ago

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