Probability of Mutualy Free Events

Mutualy free events is an event that does not affect to the other events. Suppose that the occurrence of an event A does not affect the occurrence of event B and vice versa. So the Probabiliy of the free events are an opportunity of two events that do not affect each other between events.

Probabiliy formula of mutualy free events

P(A∩B) = P(A) x P(B)

Information :

P(AnB) = Probability occurrence A and occurrence B
P(A) = Probability occurrence A
P(B) = Probability occurrence B

Probabiliy example of mutualy free events

On throwing a dice at once. A is the incident appearance the dice numbers 3 on the first dice and B is the incident appearance the dice number 5 of second dice. so what is the probability of issuing dice number 3 on the first dice and the dice number 5 on the second dice?

Resolution :
S = {(1, 1), (1, 2), (1, 3),..., (6, 6)}
n(S) = 36

A = {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)}
n(A) = 6
P(A) = n(A)/n(S)
P(A) = 6/36
P(A) = 1/6

B = {(1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (5, 6)}
n(B) = 6
P(B) = n(B)/n(S)
P(B) = 6/36
P(B) = 1/6

P(A∩B) = P(A) x P(B)
P(A∩B) = (1/6) x (1/6)
P(A∩B) = 1/36
P(A∩B) = 0.028

So the probability of issuing dice number 3 on the first dice and the dice number 5 on second dice is 0.028.

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