# Probability Calculator & Simulator / Tool

**1 times or more**

after

**100 trials**of probability

**1%**

**≈ 63.4%**

Challenger | Result |
---|---|

1th person | 0times |

2th person | 0times |

3th person | 0times |

4th person | 0times |

5th person | 0times |

6th person | 0times |

7th person | 0times |

8th person | 0times |

9th person | 0times |

10th person | 0times |

11th person | 0times |

12th person | 0times |

13th person | 0times |

14th person | 0times |

15th person | 0times |

16th person | 0times |

17th person | 0times |

18th person | 0times |

19th person | 0times |

20th person | 0times |

21th person | 0times |

22th person | 0times |

23th person | 0times |

24th person | 0times |

25th person | 0times |

26th person | 0times |

27th person | 0times |

28th person | 0times |

29th person | 0times |

30th person | 0times |

31th person | 0times |

32th person | 0times |

33th person | 0times |

34th person | 0times |

35th person | 0times |

36th person | 0times |

37th person | 0times |

38th person | 0times |

39th person | 0times |

40th person | 0times |

41th person | 0times |

42th person | 0times |

43th person | 0times |

44th person | 0times |

45th person | 0times |

46th person | 0times |

47th person | 0times |

48th person | 0times |

49th person | 0times |

50th person | 0times |

51th person | 0times |

52th person | 0times |

53th person | 0times |

54th person | 0times |

55th person | 0times |

56th person | 0times |

57th person | 0times |

58th person | 0times |

59th person | 0times |

60th person | 0times |

61th person | 0times |

62th person | 0times |

63th person | 0times |

64th person | 0times |

65th person | 0times |

66th person | 0times |

67th person | 0times |

68th person | 0times |

69th person | 0times |

70th person | 0times |

71th person | 0times |

72th person | 0times |

73th person | 0times |

74th person | 0times |

75th person | 0times |

76th person | 0times |

77th person | 0times |

78th person | 0times |

79th person | 0times |

80th person | 0times |

81th person | 0times |

82th person | 0times |

83th person | 0times |

84th person | 0times |

85th person | 0times |

86th person | 0times |

87th person | 0times |

88th person | 0times |

89th person | 0times |

90th person | 0times |

91th person | 0times |

92th person | 0times |

93th person | 0times |

94th person | 0times |

95th person | 0times |

96th person | 0times |

97th person | 0times |

98th person | 0times |

99th person | 0times |

100th person | 0times |

## 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

$1-0.99=0.01=1\%$

-> About 1 in 100 hit.

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

$1-0.99^{100}=1-0.36603...=0.63397...\approx63.4\%$

-> 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.

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

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

Probability of not hitting once:

$P_0={}_{100}C_0 \times 0.01^0 \times (1-0.01)^{(100-0)}$

$=1 \times 1 \times 0.99^{100}$

$\approx 0.36603$

Probability of hitting only once:

$P_1={}_{100}C_1 \times 0.01^1 \times (1-0.01)^{(100-1)}$

$=100 \times 0.01 \times 0.99^{99}$

$\approx 0.36973$

Probability of hitting two or more times:

$P=1-P_0-P_1$

$=1-0.36603-0.36973$

$=0.26424$

$\approx 26.42\%$