In a blue box are the numbers 3 and 5. In a red box are the numbers 4, 5 and 12. While in a green box are the numbers 5 and 13. Suppose we will assign values to x, y, and z by choosing their values from these boxes. The value of x will be chosen from the blue box. The value of y from the red box and the value of z from the green box. What is the probability that a triangle can be formed with sides of x, y, and z?

50%

Step-by-step explanation:

For x, y, and z to form a triangle, the sum of the shorter sides must be greater than the longest side.

The total number of combinations is:

2 * 3 * 2 = 12

Write out each combination, and check if they can form a triangle.

3, 4, 5: yes

3, 4, 13: no

3, 5, 5: yes

3, 5, 13: no

3, 12, 5: no

3, 12, 13: yes

5, 4, 5: yes

5, 4, 13: no

5, 5, 5: yes

5, 5, 13: no

5, 12, 5: no

5, 12, 13: yes

Of the 12 combinations, 6 can form triangles. So the probability is 6/12 or 50%.