Probability Calculator

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?

“It is the likelihood of an independent event or more than one event 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:

The following probability formulas are based upon the likelihood of two independent random events A and B, such that:

Probability Range:

0 ≤ P(A) ≤ 1

Rule of Addition:

P(A∪B) = P(A) + P(B) – P(A∩B)

Rule of Complementary Events:

P(A’) + P(A) = 1

Disjoint Events:

P(A∩B) = 0

Independent Random Events:

P(A∩B) = P(A) ⋅ P(B)

Conditional Probability:

P(A | B) = P(A∩B) / P(B)

Bayes Formula:

P(A | B) = P(B | A) ⋅ P(A) / P(B)

The calculator above also considers these equations to either calculate the probability of events or of a certain event with respect to another.

Complements: (A’ & B’):

Suppose you have two probabilities as A and B such that:

P(A’) = Probability of event denoted by P(A’) does not happen
P(B’) = Probability of event denoted by P(B’) does not happen

Example:

If the probability of an exclusive event that Jack did not come to the college is 0.24, then the probability that Jack came to the college is:

P(A') = 1 - P(A) = 1 - 0.24 = 0.76

Intersection of A & B:

Intersection probability

Intersection means the joint probability of two or more events that exclusively occur at a time, as shown in the above Venn diagram.

Example:

Make a supposition that you have 15 marbles in a bag. Out of these, 3 are violet in color and 12 are red. What is the joint probability of all the marbles?

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

The probability of drawing a red marble given that a violet marble is given as: P(B|A) = 12/14 P(B|A) = 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

Union means the occurrence of all the exclusive independent events and is calculated by a probability calculator based on the expression:

P(A U B) = P(A) + P(B) - P(A ∩ B)

Example:

Suppose you rolled a dice for which you need to calculate the probability that the number rolled is either odd or multiple of 2. So 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 multiple of 2:

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

P(A ∩ B) = 0

So we have:

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 calculator above is very simple to use. It needs certain commands as inputs to calculate results that include:

Data You Need To Enter:

Select the type of probability you need to calculate
Now provide the necessary values in their respective fields
Tap the "CALCULATE" button

Outcomes You Will Get:

The probability calculator gives you the likelihood of the occurance of one independent random event with respect to another event. These results include:

Probability of event that occurs P(A) and does not occur P(A') in both decimal and percentage

With that, the calculator figures out likelihood of different probability matches that include:

Both events occurring P(A ∩ B)
Either events occurring P(A ∪ B)
Conditional Probability P(A | B)
Either events occurring P(A ∪ B)
A or B occurs but not both P(AΔB)
Neither A nor B occurring P((A∪B)')
B occurring but not A

FAQ's:

How Do You Find Probabilities With Percentages?

To find probability as a percentage, first calculate the probability using the usual method. Then convert the result into a percentage by multiplying it by 100 and adding the percent sign (%).

If I Roll a Dice 6 Times What Is The Probability?

There is a 66.5 percent chance of it landing on a 6 at least once.

How Do I Convert Odds To Percentage?

Convert the given odd number to equivalent decimal notation
Multiply the decimal number with 100 to get 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

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EN	TR	PL
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	Percentage	Repeat Times
occuring A
occuring B