optimally check combination of two random numbers and count occurs if they pass condition

Question

I would like to do a check of two value's random combination, that passes certain condition. I constructed a snippet, that somehow works:

from random import random
i, n = 0, 100
for _ in range(n):
    x = random()
    y = random()
    if x >= 0.5 and y >= 0.5:
         i += 1
         

But I feel like I can approach more efficiently here (ie. the variables i, x, y could be somehow omitted). I was even thinking that list comprehension could improve it more, but I must admit during creation of this one, I totally failed.

My closest approach was something like:

[lambda x,y: [random(), random()] for _ in range(n) if x >= 0.5 and y >= 0.5 ]

That unfortunately creates 100 occurrences - it looks like condition is not applied onto my x, y variables.

As it looks like I'm still a python beginner, can someone advise me, how to do it the most efficient way (smallest footprint would be the key decision here).

Answer 1

Use the sum() function.

i = sum(random() >= 0.5 and random() >= 0.5 for _ in range(n))

Booleans can be treated as integers, where True == 1 and False == 0, so the sum will be correct.

Answer 2

You make the accepted answer faster by using the fact that you don't need to generate two random numbers and can instead combine their probabilities:

p_1 = 0.5
p_2 = 0.5
p_combined = 1-(1-p_1)*(1-p_2)
sum(random() >= p_combined for _ in range(n))