This module serves as the complementary teacher's guide for the Probability Topics chapter of the Elementary Statistics textbook/collection.
The best way to introduce the terms is through examples. You can introduce the terms experiment, outcome, sample space, event, probability, equally likely, conditional, mutually exclusive events, and independent events AND you can introduce the addition rule, the multiplication rule with the following example: In a box (you cannot see into it), there are are 4 red cards numbered 1, 2, 3, 4 and 9 green cards numbered 1, 2, 3, 4, 5, 6, 7, 8, 9. You randomly draw one card (experiment). Let
$R$ be the event the card is red. Let
$G$ be the event the card is green. Let
$E$ be the event the card has an even number on it.
Event card example
List all possible outcomes (the sample space). Have students list the sample space in the form {R1, R2, R3, R4, G1, G2, G3, G4, G5, G6, G7, G8, G9}. Each outcome is equally likely. Plane outcome =
$\frac{1}{\text{13}}$ .
Find
$P(R)$ .
Find
$P(G)$ . G is the complement of R.
$P(G)$ +
$P(R)$ = _______.
$P($ red card given a that the card has an even number on it) =
$P(R\mid E)$ .This is a conditional. Pick the red card out of the even cards. There are 6 even cards.
Find
$P(R\phantom{\rule{2pt}{0ex}}\text{AND}\phantom{\rule{2pt}{0ex}}E)$ . (Multiplication Rule:
$P(\text{R and E})=P(E\mid R)(P(R)$ )
Are the events
$R$ and
$G$ mutually exclusive? Why or why not?
Are the events
$G$ and
$E$ independent? Why or why not?
(Optional Topic) A
Venn diagram is a tool that helps to simplify probability problems. Introduce a Venn diagram using an example. Example: Suppose 40% of the students at ABC College belong to a club and 50% of the student body work part time. Five percent of the student body works part time and belongs to a club.
Have the students work in groups to draw an appropriate Venn diagram after you have shown them what a Venn diagram basically looks like. The diagram should consist of a rectangle with two overlapping circles. One rectangle represents the students who belong to a club (40%) and the other circle represents those students who work part time (50%). The overlapping part are those students who belong to a club and who work part time (5%).
Find the following:
$\text{P(student works part time but does not belong to a club)}$
$\text{P(student belongs to a club given that the student works part time)}$
$\text{P(student does not belong to a club)}$
$\text{P(works part time given that the student belongs to a club)}$
$\text{P(student belongs to a club or the student works part time)}$
C
student belongs to a club
Pt
student works part time
Find the following:
$\text{P(a child is 9 - 11 years old)}$
$\text{P(a child prefers regular soccer camp)}$
$\text{P(a child is 9 - 11 years old and prefers regular soccer camp)}$
$\text{P(a child is 9 - 11 years old or prefers regular soccer camp)}$
$\text{P(a child is over 14 given that the child prefers micro soccer camp)}$
$\text{P(a child prefers micro soccer camp given that the child is over 14)}$
Tree diagrams (optional topic)
A
tree is another probability tool. Many probability problems are simplified by a tree diagram. To exemplify this, suppose you want to draw two cards, one at a time,
without replacement from the box of 4 red cards and 9 green cards.
Find the following:
$\text{P(RR)}$
$\text{P(RG or GR)}$
$\text{P(at most one G in two draws)}$
$\text{P(G on the 2nd draw|R on the 1st draw)}$ . The size of the sample space has been reduced to
$12+36=481$ .
$\text{P(no R on the 1st draw)}$
Introduce
contingency tables as another tool to calculate probabilities. Let's suppose an owner of a soccer camp for children keeps information concerning the type of soccer camp the children prefer and their ages. The data is for 572 children.
Type of Soccer Camp Preference
Under 6
6-8
9-11
12-14
Over 14
Row Total
Micro
42
76
46
25
10
199
Regular
8
68
92
105
100
373
Column Total
50
144
138
130
110
572
Assign practice
Assign
Practice 1 and
Practice 2 in class. Have students work in groups.
Assign lab
The Probability Lab is an excellent way to cement many of the ideas of probability. The lab is a group effort (3 - 4 students per group).
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?