Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 4, Section 2
Some examples:
Experiment Event
----------------------- -------------------------
Roll two dice Get doubles
Roll two dice Get a `9'
Roll one die Get a `9' (a null event)
Randomly select a manufactured product It is defective
Have a child The child is a girl
Hire a new employee Employee stays at least 5 yrs
A single outcome is an example of an event. The latter concept
is more general, and can consist of multiple outcomes. For
instance, in rolling two dice you might consider the outcome
(also event) of getting a `9' or the event of getting at least a
`7' (which can be thought of as the collection of 6 distinct
outcomes: getting a `9', `10', `11' or `12').
Notice, however, that underlying this example is the assumption that my sample space consists of the individual sums of the dots on the two die - namely, S = {2, 3, 4, 5, 6, ..., 12}. That is, I've decided to make the sum of the dots the basic (building-block) level. If, instead, I were to consider the building blocks to be the individual rolls - that is, if I thought of my sample space as S = {(1,1), (1,2), (1,3), (1,4),(1,5), (1,6), (2,1), ..., (2,6), ..., (6,1), ..., (6,6)} - then a roll of the sum `9' would become an event rather than an outcome, and would consist of the outcomes {(3,6), (4,5), (5,4), (6,3)}.
Disjoint events A and B are events which have no outcomes
in common (i.e., they do not overlap in a Venn diagram). If
selecting a life-form at random, the events
$A = $ life-form is human
$B = $ life-form is a bird
are disjoint events, since no life-form can be both.
Disjoint-ness makes it easy to find p(A or B)
via the addition rule.
Two events A and B can be independent and still overlap. For instance, it is unlikely that, dealt a random card from a regular deck, the suit of the card affects the denomination (`A', `2', ..., `K'). Thus, the events
$A = $ card is a club $B = $ card is an aceare independent, though they certainly do overlap (the ace of clubs is an outcome that is in the event ``A and B"). Independence makes it easy to find p(A B) via the multiplication rule.