What's the probability of forming a triangle by breaking a stick twice?

Questions: Supposed that you have 2 chances to break a stick with length of 1 into 3 pieces. What is the probability that the 3 pieces form a triangle?

Code in Python:

[in:]

n=100
y>0
z>0
success = 0
fail = 0
n=1500

for i in range(0,1500):
    x = rd.random()
    y = rd.random()
    if (y>0.5 and x<0.5 and y-x<0.5) or (x>0.5 and y<0.5 and x-y<0.5):
        success = success+1
        
    else:
        fail = fail+1

probability = success/n
print(probability)



[out:]
0.24