Probability Calculator & Simulator / Tool

Settings & Calculate
Probability of hitting 1 times or more
after 100 trials of probability 1%
A simulation of "keeps trying until probability of 1% hits 1 times" is performed on 100 people.
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How to use this tool

This is a calculator for “the probability of hitting m times or more after n trials of probability p” and a simulator that “keeps trying until it hits m times” with the set probability.

  • Enter the “Probability (percentage or fraction)”, “Trial”, and “Hiting”, and the calculation results will be displayed automatically.
  • Probability calculation results are rounded to the third decimal place.

Calculation Method

Probability of hitting probability p more than once in n tries

Probability of hitting more than once = 100% - Probability of not hitting once


e.g. Probability 1%, 1 try, probability of hitting at least 1

-> About 1 in 100 hit.

e.g. Probability 1%, 100 try, probability of hitting at least 1

-> About 2 in 3 hit.

Probability of hitting a probability p more than m times in n tries

If the number of times you want to hit is more than two, the calculation becomes more difficult.

  • Probability of hitting more than once = 100% - Probability of not hitting all - Probability of hitting only once
  • Probability of hitting 3 or more times = 100% - Probability of not hitting all - Probability of hitting only once - Probability of hitting only twice

The “probability of hitting only x times” can be calculated using the following formula.

P=nCx×px×(1p)(nx)P=nCx \times p^x \times (1-p)^{(n-x)}

nCx is the number of combinations to choose x out of n different ones.

nCx=n!x!(nx)!nCx={\dfrac {n!}{x!(n-x)!}}

e.g. Probability 1%, 1 try, probability of hitting 2 or more times

Probability of not hitting once:
P0=100C0×0.010×(10.01)(1000)P_0={}_{100}C_0 \times 0.01^0 \times (1-0.01)^{(100-0)}
=1×1×0.99100=1 \times 1 \times 0.99^{100}
0.36603\approx 0.36603

Probability of hitting only once:
P1=100C1×0.011×(10.01)(1001)P_1={}_{100}C_1 \times 0.01^1 \times (1-0.01)^{(100-1)}
=100×0.01×0.9999=100 \times 0.01 \times 0.99^{99}
0.36973\approx 0.36973

Probability of hitting two or more times:
26.42%\approx 26.42\%