Given 5 points inside a square of side 10 cm, what is the probability that
at least two of the points are within 8cm of each other?
Sorry, I solved the "greater than" 8 case rather than the "less than" 8 cm case.
Changing the simulation slightly, I found the likelihood that the pigeons are pigeon-holed just right by using 100 million trials each time, where "good" means that all 5 managed to be 8 cm from each other:
prob. = 0.99999917
Looking at the probability it won't happen is more intuitive:
0.00000083 +/- 10%
Here are some runs:
8 64
good = 70
100000000 0.0000007000000
exp?
8 64
good = 76
100000000 0.0000007600000
exp?
8 64
good = 98
100000000 0.0000009800000
exp?
8 64
good = 88
100000000 0.0000008800000
exp?
8 64
good = 83
100000000 0.0000008300000
exp?
8 64
good = 77
100000000 0.0000007700000
exp?
8 64
good = 86
100000000 0.0000008600000
Edited on August 5, 2019, 8:59 pm
Solving the right problem
