Biostatistics for Animal Science

20 Biostatistics for Animal Science
The intersection A and B is an event such that the result is an even number and a number
greater than 3 at the same time. This is the set:
(A ∩ B) = {4,6}
with the probability:
P(A ∩ B) =P(4) + P(6) = 2 /6, because the probability of an event is the sum of probabilities
of the simple events that make up the set.
The union of the events A and B is an event such that the result is an even number or a
number greater than 3. This is the set:
(A ∪ B) = {2,4,5,6}
with the probability
P(A ∪ B) = P(2) + P(4) + P(5) + P(6) = 4 /6
Figure 2.1 presents the intersection and union of the events A and B.
Event A
Event B
2 4 5 4
6
6
A ∩ B
2 4
6
A ∪ B
Figure 2.1 Intersection and union of two events
5
A conditional probability is the probability that an event will occur if some assumptions are
satisfied. In other words a conditional probability is a probability that an event B will occur
if it is known that an event A has already occurred. The conditional probability of B given A
is calculated by using the formula:
P
( B | A)
P(
A∩
B)
=
P(
A)
Events can be dependent or independent. If events A and B are independent then:
P(B | A) = P(B) and P(A | B) = P(B)
If independent the probability of B does not depend on the probability of A. Also, the
probability that both events occur is equal to the product of each probability: