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# How to Calculate Probability of Combinations?

How to do you calculate probability of combinations?

## Probability Calculation

Probability is a branch of mathematics used to measure the likeliness of an event to occur within the total number of possibilities. Consider for example, in tossing a coin once, the probability of getting the head is one.

Formula :
Probability of Combinations = Number of favorable outcomes / Total number of outcomes

Step 1: Let us consider a 6 sided dice is rolled twice.
What is the probability of getting a sum of 5 ?
The total number of events when the dice is rolled once = 6.
It is rolled twice and hence the total number of events = 6 x 6 = 36
Total Outcomes = {(1,1), (1,2), (1,3), (1,4) , (1,5) , (1,6) , (2,1), (2,2), (2,3), (2,4) , (2,5) , (2,6), (3,1), (3,2), (3,3), (3,4) , (3,5) ,(3,6),(4,1), 4,2), (4,3), (4,4) ,(4,5) , (4,6),(5,1), 5,2), (5,3), (5,4) , (5,5) , (5,6),(6,1), (6,2), (6,3), (6,4) , (6,5) , (6,5) , (6,6)}
Total number of outcomes, n(S) = 36
Possibilities outcomes with sum 5 = [(1,4), (2,3),(3,2),(4,1)]
Number of favorable outcomes = 4

Step 2: Substituting the values in the formula,
Probability of Combinations, P (Sum of two values is 5) = Number of favorable outcomes / Total number of outcomes
P = 4 / 36
P = 1/ 4
Hence, 1/4 is the probability of getting a sum of 5 on adding the two values.

Find the probability of combinations using online probability calculator.