Transcript Jeopardy(Ch7) Probability-Distribution

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Distributions
Geo./Binomial
Distribution
Geo./Binomial
Distributions
Geo/Hypergeometric
Distributions
Various
Distributions
Various
Geo/Binomial Geo/Binomial Geo/HyperDistributions Distributions Distributions geometric Distributions
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Distributions
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CATEGORY 1 - $100
Prize
$250000
Number of
Prizes
1
$25 000
2
$2 500
5
$250
20
$25
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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 1 - $200
Identify possible random variables (x)
for the following experiments and the
possible values that the random
variable may take.
a) Tossing a coin.
b) rolling a die
c) Dealing five cards from a standard deck
CATEGORY 1 - $300
Identify possible random variables (x)
for the following experiments and the
possible values that the random
variable may take and identify their
probability distribution
a) Waiting for the first correct answer to a
question.
b) Checking baskets of fruit for overripe fruit.
CATEGORY 1 - $400
In a family with four children,
determine the probability distribution
for the number of boys and the
expected number of boys?
CATEGORY 1 - $500
Which die has the higher expectation?
A: a four-sided die with its faces
numbered 4, 12, 20, and 24
B: a six-sided die with its faces
numbered 6, 8, 14, 16, 22, and 26
CATEGORY 2 - $100
A salesperson estimates that 30% of the
people who come into the store make a
purchase. Find the binomial distribution
for the number of sales if 10 people
come into the store.
CATEGORY 2 - $200
The probability of winning a prize in a
game is 0.2. If the game will be played
1000 times during the fair, how many
prizes should the game operators keep in
stock?
CATEGORY 2 - $300
An examination consists of 50
multiple-choice items, each with 4
possible answers. What is the
probability of guessing 2 or more
correct answers?
CATEGORY 2 - $400
A Department store promotion
involves scratching four boxes on a
card to reveal randomly printed letters
from A to F. The discount is 10% for
each A reveal, 5% for each B revealed,
and 1% for the other four letters. What
is the expected discount for this
promotion.
CATEGORY 2 - $500
A bank found that 25% of its loans to new
small businesses become delinquent. Ten small
businesses are selected randomly from the
bank’s files.
a) What is the probability that three of them
are delinquent?
b) What is the probability that at least three
of them are delinquent?
c) What is the expected delinquency?
CATEGORY 3 - $100
Explain why rolling a die until a 3 shows
can be modeled by a geometric
distribution.
CATEGORY 3 - $200
In a shoot out in a basketball competition, a
player scores on 8 out ten of his shots.What is
the probability that the player will not miss
the goal until his tenth try?
CATEGORY 3 - $300
In order to start a particular board
game, a player must roll a 1 or a 6.
Show the probability distribution for
the number of rolls required to start, up
to 5 rolls.
CATEGORY 3 - $400
Suppose that an intersection you pass on the
way to school has a traffic light that is green for
40s and then amber or red for a total of 60s.
What is the probability that the light will be
green when you reach the intersection at least
once a week?
Remember: there are 5 days in a school week, therefore
we need to look at P(0 < x < 4)
CATEGORY 3 - $500
Mr. Kodsi provides Pizza for his class if
they earn an A+ average on any test. The
probability of the class getting an A+
average on one of his tests is 8%.
a)What is the probability that the class will
earn a Pizza on the fifth test.
b)What is the probability that the class will
NOT earn a Pizza for the first seven test.
CATEGORY 4 - $100
From a standard deck five cards are
randomly dealt. Show the
probability distribution of the
number of cards dealt that are
5 to 10 or Jack, King or Queen.
CATEGORY 4 - $200
Suppose that a 6-member civil
court jury was chosen from nine
men and nine women. What is the
expected number of women on the
jury?
CATEGORY 4 - $300
A bag contains two red, five black, and four
green marbles. Four marbles are selected at
random, without replacement. Calculate the
probability that exactly two are green.
CATEGORY 4 - $400
A bag contains two red, five black, and
four green marbles. Four marbles are
selected at random, without
replacement. What is the expected
numbers of red, black and green
marbles
CATEGORY 4 - $500
When can you use the binomial
distribution as an approximation to the
hypergeometric distribution.
CATEGORY 5 - $100
Determine if a uniform, binomial,
geometric, or hypergeometric
distribution would be the best model
counting the number of spades in a
hand of five cards dealt from a wellshuffled deck Explain your
reasoning.
CATEGORY 5 - $200
Determine if a uniform, binomial,
geometric, or hypergeometric
distribution would be the best model
predicting the number of tails when
flipping a coin 30 times. Explain
your reasoning.
CATEGORY 5 - $300
A fast-food chain includes one of five
different toy cars with every kid’s meal. Each
toy car is equally likely to be included with the
meal. Is it possible to specify the type of
distribution for this question? Why or why no?
CATEGORY 5 - $400
Explain the difference between a
Binomial distribution and a
Geometric distribution?
CATEGORY 5 - $500
What is the best strategy for
solving ANY Distribution
question?
CATEGORY 1 - $100
Answer
$0.14
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CATEGORY 1 - $200
Answer
a) H or T
b) 1,2,3,4,5,6
c) 1,2,3,…,10, Jack, Queen, King
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CATEGORY 1 - $300
Answer
a) X = 1, 2, 3, … (doesn’t end)
P(x) = 0.5, 0.25, 0.125, 0.0625
b) X = 0, 1, 2, 3, … , n (number of fruit)
P(x) = Discuss
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CATEGORY 1 - $400
Answer
a) x: 0, 1, 2, 3, 4
P(x): 0.0625, 0.25, 0.375, 0.25, 0.0625
b) E(x)=2
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CATEGORY 1 - $500
Answer
6-sided die
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CATEGORY 2 - $100
Answer
x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
P(x): 0.0282, 0.1211, 0.2335,
0.2668, 0.2001, 0.1029, 0.0368,
0.0090, 0.0014, 1.3778  104,
6
5.9049  10
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CATEGORY 2 - $200
Answer
200 or more
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CATEGORY 2 - $300
Answer
0.99998
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CATEGORY 2 - $400
Answer
12.6%
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CATEGORY 2 - $500
Answer
a) 0.2503
b) 0.4744
c) 2.5
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CATEGORY 3 - $100
Answer
The trials are independent and have two
possible outcomes, with the probability of
these outcomes being constant in each
trial. We are concerned with the waiting
time until a 3 is rolled, so a geometric
distribution is necessary.
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CATEGORY 3 - $200
Answer
0.026 84
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CATEGORY 3 - $300
Answer
x: 0, 1, 2, 3, 4, 5
P(x): 0.3333, 0.2222, 0.1481,
0.098 77, 0.065 84, 0.043 90
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CATEGORY 3 - $400
Answer
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CATEGORY 3 - $500
Answer
a)
b)
0.0573
0.5578
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CATEGORY 4 - $100
Answer
x: 0, 1, 2, 3, 4, 5
P(x): 0.001 68, 0.025 21, 0.135 75, 0.329
67, 0.362 64, 0.145 05
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CATEGORY 4 - $200
Answer
3 women
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CATEGORY 4 - $300
Answer
0.3818
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CATEGORY 4 - $400
Answer
1 (or 0.73) red
2 (or 1.82) Black
1 (1.454) Green
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CATEGORY 4 - $500
Answer
If n is very large, no replacement of
successes will change the ratio of
successes of the population a great
deal, and a binomial distribution will
be a good approximation to the
hypergeometric distribution.
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CATEGORY 5 - $100
Answer
Hypergeometric, because there is
various outcomes, within the
specified trials.
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CATEGORY 5 - $200
Answer
Binomial, because the trials are
specified and there is only success or
failure.
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CATEGORY 5 - $300
Answer
No it is not possible because we are not
given a specified number of trials or asked
for a waiting time.
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CATEGORY 5 - $400
Answer
Binomial Distribution has success or failure,
and the number of trials are specified.
Geometric Distribution has success or failure,
number of trials before a specific outcome
(success). The difference is the waiting time,
the number of failure trials before success
occurs.
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CATEGORY 5 - $500
Answer
1. Number of outcomes: Success
or Failure or more
2. Number of trials or Waiting
time
3. Dependent or independent
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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
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Contestant 2
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Contestant 3
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JEOPARDY! Slide Show
Setup
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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 “Edit”menu 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...
JEOPARDY! Slide Show
Setup continued
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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.
Running the JEOPARDY!
Slide Show
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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.