Question

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?

Answer 1

The probability that a triangle can be formed with sides of x, y, and z is 8/18, or approximately 0.44.

Step-by-step explanation:

To determine the probability that a triangle can be formed with sides of x, y, and z, we need to consider the conditions for triangle formation. In order for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the third side. Let's analyze the possible combinations of x, y, and z values and count how many satisfy this condition:

• If x is 3, the sum of y and z must be greater than 3.
• If y is 4 or 5, the sum of x and z must be greater than y.
• If z is 5 or 13, the sum of x and y must be greater than z.

Counting the valid combinations, we find that there are 8 combinations out of a total of 18 possible combinations. Therefore, the probability that a triangle can be formed is 8/18, or approximately 0.44.

Answer 2

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%.