Probability of 3 Events Calculator

Probability of 3 events calculator calculates the various probabilities based on three independent events.

Probability of Exactly One Event Out of 3

To calculate exactly one event out of 3, we need to know the chance of one event happening, but the other two doesn't happen.

For instance, the probability for event A to happen, but event B and event C don't happen,m
that is P(A)x[1-P(B)]x[1-P(C)].

The probability for event B to happen, but event A and event C don't happen,
that is P(B)x[1-P(A)]x[1-P(C)].

The probability for event C to happen, but event A and event B don't happen,
that is P(C)x[1-P(B)]x[1-P(A)].

Finally, combine the probabilities of 3 independent events to get exactly one event probability out of 3.

P(A)x[1-P(B)]x[1-P(C)]+P(B)x[1-P(A)]x[1-P(C)]+P(C)x[1-P(B)]x[1-P(A)].


Example:
For example, if the probability for event A is 0.5, the probability for event B is 0.35, and the probability for event C is 0.76.

The probability for exactly one of the three events happening is:

P(A)x[1-P(B)]x[1-P(C)]+P(B)x[1-P(A)]x[1-P(C)]+P(C)x[1-P(B)]x[1-P(A)]
=0.5x(1-0.35)x(1-0.76)+0.35x(1-0.5)x(1-0.76)+0.76x(1-0.35)x(1-0.5)
=0.367
=36.7%

Probability of At Least One Event Out of 3

There are two methods to calculate probabilities of at least one event out of 3.

The first method:
Calculate the probability of one event plus the probability of two events plus the probability of all 3 events.
This method requires a lot of calculation, here we will use the second method.

The second method:
Calculate the probability that all 3 events not happening. That is
[1-P(A)]x[1-P(B)]x[1-P(C)]

on the other hand, the probability remaining from all events not happening is at least one event will happen.

which is calculated as:
1-[1-P(A)]x[1-P(B)]x[1-P(C)]


Example:
For example, if the probability for event A is 0.5, the probability for event B is 0.35, and the probability for event C is 0.76.

1-[1-P(A)]x[1-P(B)]x[1-P(C)]
=1-(1-0.5)x(1-0.35)x(1-0.76)
=0.922
=92.2%