Biostatistics for Animal Science

16 Biostatistics for Animal Science
2. The sum of the probabilities of all simple events is equal to 1:
Σi P(Ei) =1
Example: Assume an experiment consists of one throw of a die. Possible results are 1, 2, 3,
4, 5 and 6. Each of those possible results is a simple event. The probability of each of those
events is 1 /6, i.e., P(E1) = P(E2) = P(E3) = P(E4) = P(E5) = P(E6). This can be shown in a
table:
Observation Event (Ei) P(Ei)
1 E1 P(E1) = 1 /6
2 E2 P(E2) = 1 /6
3 E3 P(E3) = 1 /6
4 E4 P(E4) = 1 /6
5 E5 P(E5) = 1 /6
6 E6 P(E6) = 1 /6
Both rules about probabilities are satisfied. The probability of each event is ( 1 /6), which is
less than one. Further, the sum of probabilities, Σi P(Ei) is equal to one. In other words the
probability is equal to one that any number between one and six will result from the throw
of a die.
Generally, any event A is a specific set of simple events, that is, an event consists of one or
more simple events. The probability of an event A is equal to the sum of probabilities of the
simple events in the event A. This probability is denoted with P(A). For example, assume
the event that is defined as a number less than 3 in one throw of a die. The simple events are
1 and 2 each with the probability ( 1 /6). The probability of A is then ( 1 /3).
2.2 Counting Rules
Recall that probability is:
P = number of favorable trials / total number of trials
Or, if we are able to count the number of simple events in an event A and the total number
of simple events:
P = number of favorable simple events / total number of simple events
A logical way of estimating or calculating probability is to count the number of favorable
trials or simple events and divide by the total number of trials. However, practically this can
often be very cumbersome, and we can use counting rules instead.