3. Basic probability concepts

(observations or entities) from an infinite population of outcomes that are either ‘heads’ or
‘tails’, in equal proportions.
In estimating probabilities it is useful to classify events as simple or compound. A simple
event cannot be subdivided further into component events, while a compound event comprises
two or more simple events. Whether a particular event is simple or compound may depend on
the purpose or context of the experiment. For a card drawn from a deck, for example, the event
‘diamond’ is simple by this definition, but ‘queen of diamonds’ can be considered to be
compound because the card is both a ‘queen’ (one event) and a ‘diamond’ (second event).
Alternately, ‘queen of diamonds’ might be considered to be simple because it describes one
particular outcome out of 52. Similarly, for an organism sampled from a population, the event
‘female’ is simple, but ‘adult female’ can be considered to be either compound or simple,
depending on context. We will consider this distinction in more detail below.
Sample spaces
The set of all possible outcomes of an experiment is known as the sample space of the
experiment, denoted by S. The simplest sample spaces are those in which the outcomes are
discrete. If the experiment consists of flipping a coin, then S = { H,
T}
, where H means that the
outcome of the toss is a head, and T that it is a tail. If the experiment consists of tossing a die,
then the sample space is S = { 1, 2, 3, 4, 5, 6}
. If the experiment consists of flipping two coins
(either sequentially or simultaneously), the sample space is S = {( H, H) ,( H, T)( , T, H)( , T,
T)
}.
The sample space for throwing two dice is:
( 1,1 ), ( 1, 2 ), ( 1, 3 ), ( 1, 4 ), ( 1, 5 ), ( 1, 6)
( 2,1 ), ( 2, 2 ), ( 2,3 ), ( 2, 4 ), ( 2,5 ), ( 2,6)
( 3,1 ), ( 3, 2 ), ( 3,3 ), ( 3, 4 ), ( 3,5 ), ( 3, 6)
( 4,1 ), ( 4, 2 ), ( 4,3 ), ( 4, 4 ), ( 4,5 ), ( 4,6)
( 5,1 ), ( 5, 2 ), ( 5,3 ), ( 5, 4 ), ( 5,5 ), ( 5,6)
( 6,1 ), ( 6, 2 ), ( 6,3 ), ( 6, 4 ), ( 6,5 ), ( 6,6)
⎧
⎫
⎪
⎪
⎪
⎪
⎪
⎪
S = ⎨ ⎬
⎪
⎪
⎪
⎪
⎪
⎪
⎪⎩
⎪⎭
Similarly, if the experiment consists of forming a diploid condition at a Mendelian locus
with two alleles by sampling and combining two gametes, the sample space of the alleles is
S = A,
A and the sample space of the diploid locus is
{ 1 2}
{( 1, 1) ,( 1, 2) ,( 2, 1) ,( 2,
2)
}
S = A A A A A A A A .
Sample spaces can also be defined for continuous scales. If the experiment consists of
measuring the lifetime of an organism, then there are an infinite number of possible outcomes
S = 0 < time of death