knowing how to use probability

1. 1
Probability
Par 9.7 page 699
Information 7 March 2013
– Check Edulink for memos and MORE INFO
on “Counting Principles” & “Probability”.
– No official lecture on Tuesday 12 March.
Reading work from X-Kit, Chapter 1, 2 & 3.
– Tutorial on Wednesday 13 March at 14:40 for
revision (attendance not compulsory).
– No homework task or class test next week.
– Semester Test on Thursday 14 March.
What you should learn …
How to find the probabilities of:
• Simple events.
• Mutually exclusive events.
• Independent events & “Not
Independent” events.
• Complement of an event.
Theory (sample space, events, union, intersection,
mutually exclusive, complement, independent)
3
You should be able to …
• Solve theory questions on probability.
• List possibilities as Sets.
• Solve questions working with Venn
Diagrams.
• Solve questions working with Tree
Diagrams.
• Solve questions working with Two-way
Contingency Tables.
4
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 5
J
J
J
B
K
Q
A
J
A  B
If A and B are events, their UNION, written A  B, is the event “A or B”
consisting of all outcomes in A or in B or in both A and B.
A  B = {J, J, J, J, Q, K }
Example: A card is drawn at random from a standard
deck of 52 cards.
A: getting a club face card B: getting a jack.
List the outcomes for the event of getting a club face card or
getting a jack.
Example: Union of Two Events
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 6
If A and B are events, their INTERSECTION, written A  B, is the
event “A and B” consisting of all outcomes common to both A and B.
Example: A card is drawn at random from a standard deck of 52
cards.
A  B = {J}
A: getting a club face card
List the outcomes for the event of getting a club face card and
getting a jack.
B: getting a jack.
J
K
Q
A
J
J
J
B
A  B
Example: Intersection of TwoEvents

2. 2
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 7
B
Probabilityof Union of Two Events
).()()()( BAPBPAPBAP 
If A and B are events, the probability of “A or B” is:
A
– n(A  B)
+ +
A  B
= ( + ) + ( + ) –
n(A  B) = n(A) + n(B)
Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 8
Probabilityof Union of Mutually Exclusive Events
).()()( BPAPBAP 
If A and B are MUTUALLY EXCLUSIVE, then
A B
n(A  B)
+
A and B are mutually exclusive
A  B = 0
= n(A) + n(B)
= +
Independent Events /
“Not” Independent Events
Independent Events: where the outcome of the
second event is not affected by the outcome of
the first, “WITH REPLACEMENT”.
Not independent events: where the outcome of
the second event is affected by the outcome of
the first, “WITHOUT REPLACEMENT”.
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Example
There are 5 white balls and 3 yellow balls in a
box. Select 2 balls in succession from a box
with replacement and then without
replacement. Determine the probability of
selecting:
1. 2 yellow balls.
2. 1 white and 1 yellow ball.
3. At least 1 white ball.
10
Example
The Ace, King and Queen of Diamonds are
drawn from a pack of playing cards and are
not replaced. Determine the probability of
drawing:
1. Another Ace.
2. Another Diamond.
3. The Ace of Spades.
4. A card greater than 10.
11
Grading of public schools by 1011 adults in
a survey
1. Calculate the number
of adults who gave
public schools a B.
2. What is the probability
that the adult will give
the public schools an
A?
3. What is the probability
the adult will give the
public schools a C or a
D?
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3. 3
Example
An investigation into sports participation cricket (C) ,Soccer
(S) and Volleyball (V) of 240 students at a school yielded the
following information:
• 13 disabled students cannot participate in any of the sports.
• 40 participated in all three sports.
• 67 participated in Volleyball (V), but not Cricket (C) or
Soccer (S).
• 77 participated in Soccer and Volleyball.
• 51 participated in Cricket and Soccer.
• 154 participated in Volleyball and 120 in Soccer.
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Questions
1. Draw a Venn-Diagram to illustrate the
above information (let the number that play
Cricket only be x).
2. Show that 30 students play cricket only.
3. How many students do not play Soccer?
4. What is the probability that a student chosen
at random does not play Cricket or Soccer?
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Two-Way Table: A travel agent did a
survey amongst his clients as to which type
of holiday they prefer.
Game
Reserve
Sea Travel Total
Male 450 100 X 700
Female 150 150 75 X
Total 600 X X X
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Questions
1. Complete the two-way table.
EVENT A: a person is male
EVENT B: a person prefers a game reserve
holiday.
2. Are events A and B mutually exclusive?
Explain your answer.
3. Are events A and B independent? Show
the necessary calculations.
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Questions
4. If a person is selected at random what is
the probability that the person:
• Is not male and prefers traveling holidays.
• Prefers game reserve or sea holidays.
• Is female or prefers sea holidays?
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Example
In a game of Lotto 4 numbers are drawn from
10 numbers. In how many ways can this be
done if:
1. The draw takes place without replacement
and where the ordering is important.
2. The draw takes place without replacement
and where the ordering is not important?
3. The draw takes place with replacement?
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4. 4
Example
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