How to Calculate and Solve for Mutually Non-Exclusive | Probability

The image above represents mutually non-exclusive.

To compute for mutually non-exclusive, four essential parameters are needed and these parameters are xA, NA, xB and NB.

The formula for calculating mutually non-exclusive:

P(A or B) = P(A) + P(B) – P(A and B)

Where;

P(A or B) = Mutually Non-Exclusive
P(A) = xANA
P(B) = xBNB

Let’s solve an example;
Find the mutually non-exclusive when the xA is 10, NA is 20, xB is 5 and NB is 12.

This implies that;

xA = 10
NA = 20
xB = 5
NB = 12

P(A or B) = P(A) + P(B) – P(A and B)
P(A or B) = P(A) + P(B) – (P(A) x P(B))
P(A or B) = xANA + xBNB – (xANA x xB NB)
P(A or B) = 10 20 + 5 12 – (10 20 x 5 12)
P(A or B) = 10(12) + 5(20) (20)(12) – ((10)(5) (20)(12))
P(A or B) = 120 + 100 240 – (50 240)
P(A or B) = 220 240 – 50 240
P(A or B) = (220 – 50) 240
P(A or B) = 170 240
Dividing the numerator and denominator by 10
P(A or B) = 17 24
P(A or B) = 0.708

Therefore, the mutually non-exclusive is 0.708.

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