Probability Calculator

The probability calculator helps you to calculate the probability of an event with respect to all occurrances. The tool also figures out the probability for a single event, multiple events, two events, a series of events, and conditional events.

What Is Probability In Statistics?

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

Probability Formulas:

General:

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

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

Where;

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

Other Basic Equations:

The following probability formulas apply to two independent random events A and B, defined as:

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)

The calculator above also uses these formulas to compute either the probability of individual events or the probability of one event given another.

Complements: (A’ & B’)

Suppose you have two events, A and B, with their complements defined as:

P(A’) = Probability that event A does not occur
P(B’) = Probability that event B does not occur

Example:

If the probability of the event that Jack did not come to college is 0.24, then the probability that Jack came to college is: P(A') = 1 - P(A) = 1 - 0.24 = 0.76

Intersection of A & B:

Intersection probability

The intersection represents the joint probability of two or more events occurring together, as shown in the Venn diagram above.

Example:

Suppose you have a bag containing 15 marbles. Out of these, 3 are violet and 12 are red. What is the joint probability of these events?

Probability that a drawn marble is violet = 3/15 = 0.2
Probability that a drawn marble is red = 12/15 = 0.8

The probability of drawing a red marble given that a violet marble is drawn is: P(B|A) = 12/14 = 0.85
Intersection probability = P(A ∩ B) = P(A) × P(B|A) = (0.2) × (0.85) = 0.17

Union of A & B:

Union of probabilities

The union represents the probability of either of the independent events occurring. It is calculated using the formula:

P(A U B) = P(A) + P(B) - P(A ∩ B)

Example:

Suppose you roll a dice, and you want to calculate the probability that the number rolled is either odd or a multiple of 2. Then we have:

Dice Set = {1, 2, 3, 4, 5, 6}

Probability of an odd number:

P(A) = {1, 3, 5} = 3/6 = 1/2 = 0.5

Probability of a multiple of 2:

P(B) = {2, 4, 6} = 3/6 = 1/2 = 0.5

Intersection of A and B:

P(A ∩ B) = 0

So, the union probability is:

P(A U B) = P(A) + P(B) - P(A ∩ B)

P(A U B) = 0.5 + 0.5 - 0

P(A U B) = 1

How to Use the Probability Calculator?

The probability calculator above is very easy to use. You just need to provide some input values, and it will calculate results including:

Data You Need to Enter:

Select the type of probability you want to calculate
Enter the required values in the respective fields
Click Calculate

Results You Will Get:

The calculator provides the probability of an event occurring with respect to another event. The results include:

Probability of the event occurring P(A) and not occurring P(A'), shown in both decimal and percentage formats

Additionally, the calculator can determine the probabilities for different combinations of events, including intersections, unions, and conditional probabilities.

Probability of both events occurring P(A ∩ B)
Probability of either event occurring P(A ∪ B)
Conditional probability P(A | B)
Probability of either event occurring P(A ∪ B)
Probability of A or B occurring, but not both P(AΔB)
Probability of neither A nor B occurring P((A∪B)')
Probability of B occurring but not A

Important Questions:

How Do You Find Probabilities as Percentages?

To calculate a probability as a percentage, first solve the problem normally. Then convert your result into a percent by multiplying by 100.

If I Roll a Dice 6 Times, What Is the Probability?

There is a 66.5% chance of rolling a 6 at least once in 6 rolls.

How Do I Convert Odds to Percentages?

- Convert the given odds into decimal form
- Multiply the decimal by 100 to get the percentage

Probability Table:

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

Other languages: olasılık hesaplama, kalkulator prawdopodobieństwa, kalkulator probabilitas, wahrscheinlichkeitsrechner, 確率計算, 확률 계산기, pravděpodobnost kalkulačka, calculo de probabilidade, calcul de probabilité, calculo de probabilidad, calcolo probabilità, расчет вероятности, todennäköisyys laskuri, sandsynlighedsregning, sannsynlighetskalkulator.

EN	TR	PL
ID	DE	JA
KO	CS	PT
FR	ES	IT
RU	FI	DA
NO

EN	TR	PL
ID	DE	JA
KO	CS	PT
FR	ES	IT
RU	FI	DA
NO

	Probability	Repeat Times
Event A
Event B