Probability of combined Events

Formula of Probability of Combined Events

The Probability of Combined Events Formula can be determined by the following formula:

P(A∪B) = P(A) + P(B) - P(A∩B)

Information :

P (A) = Probability of A

P (B) = Probability of B

P (A∩B) = Probability of A slice B

P (A∪B) = Probability of A combined B

Example of Probability of combined Events

In a dice, if A is the occurrence of the odd number and B is the occurrence of the prime number.So please specify the chance of occurrence of odd or prime numbers!

Resolution:
S = {1, 2, 3, 4, 5, 6}
n(S) = 6

A = Odd numbers :{1, 3, 5}
n(A) = 3
P(A) = n(A)/n(S)
P(A) = 3/6

B = Prime numbers : {2, 3, 5}
n(B) = 3
P(B) = n(B)/n(S)
P(B) = 3/6

(A∩B) = {3, 5}
n(A∩B) = 2
P(A∩B) = n(A∩B)/n(S)
P(A∩B) = 2/6

P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = (3/6) + (3/6) - (2/6)
P(A∪B) = (3 + 3 - 2)/6
P(A∪B) = 4/6
P(A∪B) = 2/3
P(A∪B) = 0.67

So the chance of the emergence of odd numbers or prime numbers are 0.67 or 67%.

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