If there is a 2.3% chance of something happening, what are the odds it NOT happening 400 and 500 times in a row?

Question

500 is my main question but 400 would also greatly help.

Thank you very much in advance.

Answer 1

chance of not happening = 100%-2.3% = 97.7% on each time

for 400 times the chance is (.977)^400

plug that into a scientific calculator to get

9.07455814 x 10^-5 which is

0.00000907455814 or

0.000907455814% chance of never happening in 400 tries

for 500, it's (.977)^500=

8.85690241 x 10^-6 =

0.000000885690241 =

0.0000885690241% chance of never happening in 500 tries.