Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 4, Section 2



  1. Give several examples of experiments and events related to these experiments.

    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
    	
    
  2. What is the difference between an outcome and an event?

    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)}.

  3. What is the difference between disjoint (or mutually exclusive) events and independent events.

    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 ace
    	
    
    are 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.