Probability Calculator

Calculating For:

Number of Possible Outcomes:

Number of Events Occured (n)A:

Probability Calculator

The probability calculator helps you calculate the probability of events, whether for a single event, multiple events, two events, a series of events, or conditional events.

What Is Probability in Statistics?

Probability represents the chance of a single event or multiple events occurring.

Probability Formulas

General Formula:

P(A) = Number of Favorable Outcomes / Total Number of Possible Outcomes

P(A) = n(E) / n(S)

P(A) = Probability of event A
n(E) = Number of favorable outcomes
n(S) = Total number of outcomes in the sample space

Other Basic Probability Rules:

Probability Range: 0 ≤ P(A) ≤ 1
Addition Rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Complement Rule: P(A') + P(A) = 1
Disjoint (Mutually Exclusive) Events: P(A ∩ B) = 0
Independent Events: P(A ∩ B) = P(A) × P(B)
Conditional Probability: P(A | B) = P(A ∩ B) / P(B)
Bayes’ Theorem: P(A | B) = P(B | A) × P(A) / P(B)

Complements (A' & B')

For any event, the complement represents the probability that the event does not occur:

P(A') = Probability that A does not occur
P(B') = Probability that B does not occur

Example:

If the probability that Jack did not come to college is 0.24, then the probability he came is:

P(A) = 1 − P(A') = 1 − 0.24 = 0.76

Intersection of A & B

The intersection represents the joint probability of two events occurring together.

Intersection probability

Example:

Suppose a bag contains 15 marbles: 3 violet and 12 red.

P(violet) = 3/15 = 0.2
P(red) = 12/15 = 0.8

The probability of drawing a red marble given a violet marble is drawn:

P(B|A) = 12/14 ≈ 0.857

Intersection probability: P(A ∩ B) = P(A) × P(B|A) = 0.2 × 0.857 ≈ 0.17

Union of A & B

The union represents the probability that at least one of the events occurs:

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Union of probabilities

Example:

Rolling a dice: Probability of rolling an odd number or a multiple of 2.

Dice Set = {1,2,3,4,5,6}
P(odd) = {1,3,5} = 3/6 = 0.5
P(multiple of 2) = {2,4,6} = 3/6 = 0.5
P(A ∩ B) = 0 (no overlap)

P(A ∪ B) = 0.5 + 0.5 − 0 = 1

How to Use the Probability Calculator

To use the calculator, simply:

Select the type of probability to calculate
Enter the required values in the input fields
Click Calculate

The calculator outputs probabilities for various scenarios, including:

P(A) and P(A') in both decimal and percentage formats
Intersection P(A ∩ B)
Union P(A ∪ B)
Conditional probability P(A | B)
Probability of A or B but not both P(A Δ B)
Probability of neither P((A ∪ B)')

Converting Probability to Percentage

Multiply the probability value by 100. For example, P(A) = 0.76 → 76%

Dice Example:

Probability of rolling a 6 at least once in 6 rolls ≈ 66.5%

z	0	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0	0	0.00399	0.00798	0.01197	0.01595	0.01994	0.02392	0.0279	0.03188	0.03586
0.1	0.03983	0.0438	0.04776	0.05172	0.05567	0.05962	0.06356	0.06749	0.07142	0.07535
0.2	0.07926	0.08317	0.08706	0.09095	0.09483	0.09871	0.10257	0.10642	0.11026	0.11409
0.3	0.11791	0.12172	0.12552	0.1293	0.13307	0.13683	0.14058	0.14431	0.14803	0.15173
0.4	0.15542	0.1591	0.16276	0.1664	0.17003	0.17364	0.17724	0.18082	0.18439	0.18793
0.5	0.19146	0.19497	0.19847	0.20194	0.2054	0.20884	0.21226	0.21566	0.21904	0.2224
0.6	0.22575	0.22907	0.23237	0.23565	0.23891	0.24215	0.24537	0.24857	0.25175	0.2549
0.7	0.25804	0.26115	0.26424	0.2673	0.27035	0.27337	0.27637	0.27935	0.2823	0.28524
0.8	0.28814	0.29103	0.29389	0.29673	0.29955	0.30234	0.30511	0.30785	0.31057	0.31327
0.9	0.31594	0.31859	0.32121	0.32381	0.32639	0.32894	0.33147	0.33398	0.33646	0.33891
1	0.34134	0.34375	0.34614	0.34849	0.35083	0.35314	0.35543	0.35769	0.35993	0.36214
1.1	0.36433	0.3665	0.36864	0.37076	0.37286	0.37493	0.37698	0.379	0.381	0.38298
1.2	0.38493	0.38686	0.38877	0.39065	0.39251	0.39435	0.39617	0.39796	0.39973	0.40147
1.3	0.4032	0.4049	0.40658	0.40824	0.40988	0.41149	0.41308	0.41466	0.41621	0.41774
1.4	0.41924	0.42073	0.4222	0.42364	0.42507	0.42647	0.42785	0.42922	0.43056	0.43189
1.5	0.43319	0.43448	0.43574	0.43699	0.43822	0.43943	0.44062	0.44179	0.44295	0.44408
1.6	0.4452	0.4463	0.44738	0.44845	0.4495	0.45053	0.45154	0.45254	0.45352	0.45449
1.7	0.45543	0.45637	0.45728	0.45818	0.45907	0.45994	0.4608	0.46164	0.46246	0.46327
1.8	0.46407	0.46485	0.46562	0.46638	0.46712	0.46784	0.46856	0.46926	0.46995	0.47062
1.9	0.47128	0.47193	0.47257	0.4732	0.47381	0.47441	0.475	0.47558	0.47615	0.4767
2	0.47725	0.47778	0.47831	0.47882	0.47932	0.47982	0.4803	0.48077	0.48124	0.48169
2.1	0.48214	0.48257	0.483	0.48341	0.48382	0.48422	0.48461	0.485	0.48537	0.48574
2.2	0.4861	0.48645	0.48679	0.48713	0.48745	0.48778	0.48809	0.4884	0.4887	0.48899
2.3	0.48928	0.48956	0.48983	0.4901	0.49036	0.49061	0.49086	0.49111	0.49134	0.49158
2.4	0.4918	0.49202	0.49224	0.49245	0.49266	0.49286	0.49305	0.49324	0.49343	0.49361
2.5	0.49379	0.49396	0.49413	0.4943	0.49446	0.49461	0.49477	0.49492	0.49506	0.4952
2.6	0.49534	0.49547	0.4956	0.49573	0.49585	0.49598	0.49609	0.49621	0.49632	0.49643
2.7	0.49653	0.49664	0.49674	0.49683	0.49693	0.49702	0.49711	0.4972	0.49728	0.49736
2.8	0.49744	0.49752	0.4976	0.49767	0.49774	0.49781	0.49788	0.49795	0.49801	0.49807
2.9	0.49813	0.49819	0.49825	0.49831	0.49836	0.49841	0.49846	0.49851	0.49856	0.49861
3	0.49865	0.49869	0.49874	0.49878	0.49882	0.49886	0.49889	0.49893	0.49896	0.499
3.1	0.49903	0.49906	0.4991	0.49913	0.49916	0.49918	0.49921	0.49924	0.49926	0.49929
3.2	0.49931	0.49934	0.49936	0.49938	0.4994	0.49942	0.49944	0.49946	0.49948	0.4995
3.3	0.49952	0.49953	0.49955	0.49957	0.49958	0.4996	0.49961	0.49962	0.49964	0.49965
3.4	0.49966	0.49968	0.49969	0.4997	0.49971	0.49972	0.49973	0.49974	0.49975	0.49976
3.5	0.49977	0.49978	0.49978	0.49979	0.4998	0.49981	0.49981	0.49982	0.49983	0.49983
3.6	0.49984	0.49985	0.49985	0.49986	0.49986	0.49987	0.49987	0.49988	0.49988	0.49989
3.7	0.49989	0.4999	0.4999	0.4999	0.49991	0.49991	0.49992	0.49992	0.49992	0.49992
3.8	0.49993	0.49993	0.49993	0.49994	0.49994	0.49994	0.49994	0.49995	0.49995	0.49995
3.9	0.49995	0.49995	0.49996	0.49996	0.49996	0.49996	0.49996	0.49996	0.49997	0.49997
4	0.49997	0.49997	0.49997	0.49997	0.49997	0.49997	0.49998	0.49998	0.49998	0.49998

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	Percentage	Repeat Times
occuring A
occuring B