Download 82Classifying_Events

Chapter 8 Probability
8.2A
MATHPOWERTM 12, WESTERN EDITION 8.2A.1
Independent Versus Dependent Events
Two events are independent if the probability that each event will
occur is not affected by the occurrence of the other event.
Two events are dependent if the outcome of the second event is
affected by the occurrence of the first event.
Classify the following events as independent or dependent:
a) tossing a head and rolling a six
independent
b) drawing a face card, and not returning it to the deck, and
then drawing another face card
dependent
c) drawing a face card and returning it to the deck, and then
drawing another face card
independent
If the probabilities of two events are P(A) and P(B) respectively,
then the probability that both events will occur, P(A and B), is:
P(A and B) = P(A) x P(B)
8.2A.2
Finding Probability
1. A cookie jar contains 10 chocolate and 8 vanilla cookies.
If the first cookie drawn is replaced, find the probability of:
a) drawing a vanilla and then a chocolate cookie
P(V and C) = P(V) x P(C)
The probability of drawing a
8 10
vanilla and a chocolate cookie is
 
18 18
20
.
20

81
81
b) drawing two chocolate cookies
P(C and C) = P(C) x P(C)
10 10
 
18 18
25

81
The probability of drawing
two chocolate cookies is
25
.
81
8.2A.3
Finding Probability
2. Find the probability of drawing a vanilla and then drawing a
chocolate cookie, if the first cookie drawn is eaten.
P(V and C) = P(V) x P(C)
The probability of drawing a
8 10
vanilla and a chocolate cookie is
 
18 17
0.2614.
40

153
3. An aircraft has three independent computer guidance systems.
The probability that each will fail is 10-3 . What is the probability
that all three will fail?
P(all three fail) = P(A) x P(B) x P(C)
= 10-3 x 10-3 x 10-3
= 10-9
The probability that all three will fail is 10-9.
8.2A.4
Probability
The sum of all the probabilities of an event is equal to 1.
If P = 1, then the event is a certainty.
If P = 0, then the event is impossible.
In probability, if Event A occurs, there is also the probability
that Event A will not occur. Event A not occurring is the
compliment of Event A occurring.
The probability of Event A not occurring is written as P(A).
(This is read as “Probability of not A”).
For Event A: P(A) + P(A) = 1
P(A) = 1 - P(A)
Example: One card is drawn from a deck of 52 cards.
What is the probability of each of these events?
a) drawing a red four b) not drawing a red four
1
1
b ) P( not red 4 )  1 
a ) P( red 4 ) 
26
26
25

26
8.2A.5
Finding the Probability of the Same Birth Month
In a group of seven people, what is the probability that
at least two have their birthdays in the same month?
Find the probabilities of the seven birthdays being in
seven different months.
12
8
1st person 
5th person 
12
12
11
2nd person 
6th person  7
12
12
3rd person  10
6
12
7th person 
12
9
4th person 
12
6 11 10 9 8 7 6
P(birthdays in 7 different months)      
12 12 12 12 12 12 12
= 0.111
P(at least 2 birthdays in the same month) = 1 - (different months)
= 1 - 0.111
8.2A.6
= 0.889
Finding the Probability of the Same Birth Month [cont’d]
6 11 10 9 8 7 6
P(birthdays in 7 different months)       
12 12 12 12 12 12 12
= 0.111
P(at least 2 birthdays in the same month) = 1 – 0.111
= 0.889
Alternative Method:
12 x 11 x 10 x 9 x 8 x 7 x 6 can be expressed as 12P7.
12 x 12 x 12 x 12 x 12 x 12 x 12 can be expressed as 127.
P7
12
P(birthdays in 7 different months) 
127
= 0.111
P(at least 2 birthdays in the same month) 1  12 P7
127
= 0.889
8.2A.7
Suggested Questions:
Pages 380 and 381
1-6, 14, 16, 17 ab
8.2A.8
Chapter 8 Probability
8.2B
MATHPOWERTM 12, WESTERN EDITION 8.2B.9
Classifying Exclusivity
Two events are mutually exclusive if they cannot occur
simultaneously. For instance, the events of drawing a
diamond and drawing a club from a deck of cards are mutually
exclusive because they cannot both occur at the same time.
For mutually exclusive events:
P(A or B) = P(A) + P(B)
Events that are not mutually exclusive have some common
outcomes. For instance, the events of drawing a diamond and
drawing a king from a deck of cards are not mutually exclusive
because the king of diamonds could be drawn, thereby having
both events occur at the same time.
For events that are not mutually exclusive:
P(A or B) = P(A) + P(B) - P(A and B)
8.2B.10
Classifying Exclusivity
Classify each event as mutually exclusive or not mutually exclusive.
a) choosing an even number and choosing a prime number
not mutually exclusive
b) picking a red marble and picking a green marble
mutually exclusive
c) living in Edmonton and living in Alberta
not mutually exclusive
d) scoring a goal in hockey and winning the game
not mutually exclusive
e) having blue eyes and black hair
not mutually exclusive
8.2B.11
Probability and Exclusivity
1. A box contains six green marbles, four white marbles,
nine red marbles, and five black marbles. If you pick one
marble at a time, find the probability of picking
a) a green or a black marble.
P(G or B) = P(G) + P(B)
6
5


24 24
11

24
b) a white or a red marble.
P(W or R) = P(W) + P(R)
4
9


24 24
13

24
8.2B.12
Probability and Exclusivity
2. Determine the probability of choosing a diamond
or a face card from a deck of cards.
P(D or F) = P(D) + P(F) - P(D and F)
13 12 13 12
  (  )
52 52 52 52
25 3 22


52 52 52 .
22

52
The probability of choosing a diamond
22
or a face card is
.
52
8.2B.13
Probability and Exclusivity
3. A national survey revealed that 12.0% of people exercise
regularly, 4.6% diet regularly, and 3.5% both exercise and
diet regularly. What is the probability that a randomly-selected
person neither exercises nor diets regularly?
Find the probability that a person exercises or diets regularly.
P(D or F) = P(D) + P(F) - P(D and F)
= 0.12 + 0.046 - 0.035
= 0.131
Therefore, the probability that a person neither
exercises nor diets regularly is:
1 - 0.131 = 0.869
= 86.9%
8.2B.14
Probability and Exclusivity [cont’d]
Alternative method: Use a Venn diagram
A national survey revealed that 12.0% of people exercise
regularly, 4.6% diet regularly, and 3.5% both exercise and
diet regularly. What is the probability that a randomly-selected
person neither exercises nor diets regularly?
Entire Population
Dieter
Exerciser
8.5%
3.5%
1.1%
Therefore, the probability that a person neither
exercises nor diets regularly is:
100% - (8.5% + 3.5% + 1.1%) = 86.9%
8.2B.15
Suggested Questions:
Pages 380 and 381
7-13, 15, 18, 20
8.2B.16