Counting

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Counting
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Probability
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Discrete Probability Distribution
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Stats
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Continuous Probability Distribution
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Counting
Discrete Probability Distribution
Stats
Cont. Probability Distribution
Probability

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CATEGORY 1 - 100
How many letter permutations are there in each of
the following words a) MATH b) CAREER
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CATEGORY 1 - 200
a) How many four-digit numbers are possible with
the digits 3, 4, 5, 6, 7, 8, and 9? Assume that
no digits repeat. b) How many of these numbers
in part a) are odd numbers? c) How many of
these numbers in part a) are even numbers?
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CATEGORY 1 - 300
Loyalist CVI is about to have a reunion of all
the previous graduating classes. There are 20
members of the current alumni association. Of
these, eight members are recent graduates. In how
many ways can a sub-committee of four members be
struck to provide memorabilia if a) there are no
restrictions b) the sub-committee must be all
recent graduates c) the sub-committee must have
only two recent graduates d) the sub-committee
must have no more than three recent graduates
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CATEGORY 1 - 400
A soccer team played eight games and won five of
them. There were no ties. How many arrangements
of the five wins and three losses are possible?
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Every Friday a downtown restaurant has an
all-you-can-eat buffet with the following items
  soup, garden salad bread, rolls,
crackers popcorn shrimp, shrimp and
dip lasagna, chicken wraps, beef stew snow
peas, carrots, mixed vegetables fresh fruit,
apple pie, custard a) How many different
combinations of items could you choose for your
meal?b) The restaurant also has a lunch special
featuring any one item from each group. How many
choices do you have in this special?
Expand and simplify
CATEGORY 1 - 500
.
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A pencil case contains three blue pens, two red
pens, and five pencils. If you reach in and
randomly select a writing instrument, what is the
probability that it isa)a red pen? b)a
pen? c) not a blue pen?
CATEGORY 2 - 100
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Suppose that the weather forecast calls for a 30
chance of rain on each of the three days of a
long weekend. What are the odds in favour of no
rain throughout the entire long weekend?
CATEGORY 2 - 200
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A box contains 48 tickets for six door prizes.
Six tickets are drawn, and not replaced, to
declare the winners. If Serge purchases 8tickets,
determine the probability that he winsa) the
first prizeb) the first and second prizesc) all
six prizes
CATEGORY 2 - 300
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CATEGORY 2 - 400
Ten boys and 12 girls decide to rent a
16-passenger van and a 6-passenger car to drive
to a rock concert in a nearby city. If the group
is distributed randomly between the vehicles,
what is the probability that a) there are no boys
in the car? b) there are no girls in the
car? c) Steve and Susan are both in the van? d)
either Steve or Susan are in the van?
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Six friends at a dinner party are seated randomly
at a round table. What is the probability
thata) Russel will be seated next to
Sadia?b) Russel, Jade, and Sadia are seated next
to each other in alphabetical order, clockwise?
CATEGORY 2 - 500
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A lottery ticket costs 1.00 and a total of 2 250
000 tickets were sold. The prizes and their
frequencies are given in the following table.
Determine the expected winnings of each ticket.
CATEGORY 3 - 100
Prize Number of Prizes
250 000 1
25 000 2
2 500 5
250 20
25 100
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CATEGORY 3 - 200
Of 20 people invited to a pool party, 4 prefer
vanilla ice cream, 7 prefer chocolate, and 3
prefer strawberry. The host surveys six of these
people at random to determine how much ice cream
to buy. a) What is the probability that at least
3 of the people surveyed prefer chocolate ice
cream? b) What is the probability that none
prefer vanilla ice cream? c) What is the expected
number of people who prefer strawberry ice cream?
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What is the probability that at least one double
will occur within the first five rolls of two
dice?What is the expected waiting time before a
double?
CATEGORY 3 - 300
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A multiple-choice mathematics quiz has five
questions, each with five possible answers.
Someone simply guesses at each answer.a) What is
the probability of zero or one correct guesses?
b) What is the probability of getting more than
half the questions right?c) What is the expected
number of correct guesses?
CATEGORY 3 - 400
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In the spring, the Ministry of the Environment
caught and tagged 300 raccoons in an area in
cottage country. The raccoons were released after
being vaccinated against rabies. To estimate the
raccoon population in the area, the ministry
caught 25 raccoons during the summer. Of these,
10 had tags. Estimate the raccoon population in
the area.
CATEGORY 3 - 500
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Determine the mean.
CATEGORY 4 - 100
56 95 128 102 76 113
87 115 65 109 176 105
102 57 43 98 102 128
81 92 34 144 104 95
69 84 155 137 73 223
78 128 117 116 192 120
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The final mark in a data management class is
calculated using the weightings shown in the
table below.
CATEGORY 4 - 200
Quizzes 10
Assignments 10
Tests 30
Culminating Assignment 20
Exam 30
Quizzes 78 /84
Assignments 102/120
Tests 203 /250
Culminating Assignment 85 /100
Exam 76 /90
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Describe the type of sample used in each
scenario.a) a telephone survey of numbers
randomly selected from a stores database.b) A
student council asks students to comment on an
issue by placing their comments in a comment
box.c) A proportionate number of people from 10
age groups are randomly selected from the
population of a city.
CATEGORY 4 - 300
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Define or explain each of the following terms.a)
moderate positive linear correlation b) control
groupc) presumed relationship
CATEGORY 4 - 400
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Define or explain each of the following
terms. a) correlation coefficientb) coefficient
of determination
CATEGORY 4 - 500
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A cereal manufacturer finds that the mass of
cereal in the 200-g packages is normally
distributed with a mean of 200 g and a standard
deviation of 16.3 g.a) What is the probability
that a package chosen at random has a mass
between 180 g and 220 g?b) If a container with
less than 170 g is considered below standard,
what proportion of cereal packages would be
rejected?
CATEGORY 5 - 100
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A cereal manufacturer finds that the mass of
cereal in the 200-g packages is normally
distributed with a mean of 200 g and a standard
deviation of 16.3 g. Out of 500 packages, how
many have a mass greater than 230 g?
CATEGORY 5 - 200
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The probability of winning a large stuffed animal
in the ring-toss game at a fair is 10.a) Using
a binomial distribution and a normal
distribution, predict how the probabilities of
winning at least 5 of 50 games will differ.b)
Find the probability of winning at least 5 of 50
games using i) a binomial distribution ii) a
normal approximation
CATEGORY 5 - 300

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The marks on one mathematics test had a mean of
67 and a standard deviation of 4. A second
mathematics test had a mean of 65 and a standard
deviation of 9. Josh had a mark of 70 on both
tests. Which result appears to be the better
mark? Explain.
CATEGORY 5 - 400
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The marks on one mathematics test had a mean of
67 and a standard deviation of 4. A second
mathematics test had a mean of 65 and a standard
deviation of 9. The teacher has decided to bell
the marks on the first test in order to match the
mean and standard deviations of the second test.
Find Joshs new mark on the first test.
CATEGORY 5 - 500
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CATEGORY 1 - 100
Answer

1. 24 b) 180

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CATEGORY 1 - 200
Answer

1. 840 b) 480 c) 360

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CATEGORY 1 - 300
Answer

• 20C4 4845
• 8C4 70
• 8C2 x 12C 2 1848
• 4775

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CATEGORY 1 - 400
Answer
56

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CATEGORY 1 - 500
Answer

1. 65 535
2. 324

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CATEGORY 2 - 100
Answer

1. .
2. .
3. .

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CATEGORY 2 - 200
Answer

• 343657

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CATEGORY 2 - 300
Answer

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CATEGORY 2 - 400
Answer

1. 0.012
2. 0.0028
3. 0.52
4. 0.94

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CATEGORY 2 - 500
Answer

1. .
2. .

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CATEGORY 3 - 100
Answer
0.14

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CATEGORY 3 - 200
Answer

• a) 0.3359
• 0.2066
• 0.9000

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CATEGORY 3 - 300
Answer
a) 0.5981 b) 5 rolls

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CATEGORY 3 - 400
Answer

• a) 0.7373
• 0.05792
• 1

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CATEGORY 3 - 500
Answer
750 raccoons

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CATEGORY 4 - 100
Answer
mean 105 500

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CATEGORY 4 - 200
Answer
84.5

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CATEGORY 4 - 300

Answer

• simple random
• voluntary response
• c) stratified

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CATEGORY 4 - 400
Answer

• a moderate pattern in which one variable
  increases, as the other increases in direct
  proportion
• a group similar to an experimental group in a
  study, except that the independent variable in
  the study B held constant
• c) an observed correlation between two
  variables, while not seemingly accidental, the
  causal nature of which is not apparent

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CATEGORY 4 - 500
Answer

• a quantitative measure of the strength of linear
  correlation how close a line fits a set of data
• b) a quantitative measure of the strength of
  non-linear correlation how closely a curve fits
  a set of data

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CATEGORY 5 - 100
Answer
a) 78.02 b) 3.28

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CATEGORY 5 - 200
Answer
16.42 packages

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CATEGORY 5 - 300
Answer

1. Sample prediction the results using normal
   approximation will be the same, to the nearest
   tenth.
2. i)0.5688 ii) 0.5932

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CATEGORY 5 - 400

Answer
The result for test one appears to be the better
mark because it has a higher z-score the
z-score for test one is 0.75, and the z-score for
test two is 0.56.

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CATEGORY 5 - 500
Answer
71.75

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FINAL CATEGORY

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FINAL CATEGORY
INSERT FINAL QUESTION (ANSWER) HERE

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FINAL CATEGORY
WHAT OR WHO IS THE FINAL ANSWER?

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END OF GAME

• Daily Doubles and
• usage notes follow...

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Contestant 1

Contestant 2

Contestant 3

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JEOPARDY! Slide ShowSetup

• The font for the question answer slides is
  Enchanted a copy of this font in located in
  the REAL Jeopardy Template folder or included
  in the jeopardy_pc.zip file. (This font will
  need to be installed in the C/WINDOWS/FONTS
  folder of the computer running the show.) In
  order to keep all of the sounds and fonts
  together, copy the entire REAL Jeopardy
  Template folder or jeopardy_pc.zip file.
• To change the categories
• 1. Go to the Editmenu and choose Replace
• 2. In the Find box, type CATEGORY X (X being 1
  through 5) (all caps).
• 3. In the Replace box, type the category in all
  caps (for example, PRESIDENTS).
• 4. Click Replace All
• To change the dollar values (for example to
  create Double Jeopardy)
• 1. Go to the Edit menu and choose Replace
• 2. In the Find box, type X (the dollar value you
  want to change).
• 3. In the Replace box, type the new dollar value
  (with ).
• 4. Click Replace All...

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JEOPARDY! Slide ShowSetup continued

• To set up the Daily Double
• 1. Choose which dollar value(s) to set as Daily
  Double (normally, Jeopardy has one Daily Double,
  and Double Jeopardy has two).
• 2. Go to the Game Board slide (Slide 8), right
  click once on the dollar value for the
  appropriate question, choose Hyperlink, and
  choose Edit Hyperlink.
• 3. In the Edit Hyperlink window, go to Named
  location in file and click Browse
• 4. In the Hyperlink to Slide window, scroll down
  to the appropriate slide Slides 64 and 65 are
  regular Daily Doubles, Slide 66 is an Audio Daily
  Double, Slide 67 is a Video Daily Double. Click
  OK.
• 5. Go to the Daily Double slide just linked to,
  and right click once on the answer arrow at the
  bottom right, choose Hyperlink, and choose Edit
  Hyperlink.
• 6. In the Action Settings window, make sure the
  Hyperlink button (to the left of Hyperlink) is
  selected, and in the select box underneath choose
  Slide
• 7. In the Hyperlink to Slide window, scroll down
  to the appropriate question slide (the original
  slide number of the question).
• NOTE Using the Audio and Video Daily Doubles
  requires adding audio or video/picture clips to
  the question slides. If you are not familiar with
  doing this in PowerPoint, do not use those Daily
  Doubles.

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Running the JEOPARDY! Slide Show

• On the game board with the categories on top
  (Slide 8), click on the desired dollar value.
  (The first game board is used only to blink in
  the dollar values like the show.)
• The question slide will pop up the slides are
  timed with an eight-second timer. At the end of
  the timer, an alarm will chime.
• ICONS
• ? Go to the answer screen.
• House Go back to the game board.
• Right Arrow (on Daily Doubles) Go to the
  question screen.
• Right Arrow w/ Bar (on Game Board) Go to the
  Final Jeopardy category.
• Turned-up Arrow Reload question screen after
  incorrect guess.
• Go to the Scoreboard slide.
• Left Arrow (on Scoreboard) Go to the previous
  slide.