Transcript Jeopardy Review

Jeopardy
Definitions
Prob
Rules
Tables
Mixed
Rules
Misconceptions
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Final Jeopardy
$100 - Definitions
Two events that
cannot happen at the
same time.
$100 Answer from Definitions
Mutually Exclusive/ Disjoint
$200 - Definitions
The set of all possible outcomes.
$200 Answer from Definitions
Sample Space
$300 - Definitions
Knowledge of one event having
occurred does not affect the
probability of the occurrence of
the second event.
$300 Answer from Definitions
Independent
$400 - Definitions
An activity or situation in
which there is uncertainty
concerning which of two or
more possible outcomes will
result
$400 Answer from Definitions
Chance Experiment
$500 - Definitions
Probability based on the
sample space of an event
$500 Answer from Definitions
Theoretical Probability
$100 - Prob Rules
Susan took two tests. The
probability of her passing both
tests is 0.6. The probability of her
passing the first test is 0.8. What
is the probability of her passing
the second test given that she
has passed the first test?
$100 Answer from prob rules
0.75
$200 - Prob rules
Two sets of cards with a letter on each card
as follows are placed into separate bags.
Sara randomly picked one card from each
bag. Find the probability that both are
vowels?
$200 Answer from prob rules
3
15
$300 – Prob Rules
The probabilities of three teams A, B
and C winning a badminton
competition are
1 1
1
, , and respectively
3 5
9
Calculate the probability that neither
A nor B wins.
$300 Answer from Prob Rules
P(neither A nor B will win)
= 1 – P(either A or B will
win)
1 1
1   
3 5
8
7
1 
15 15
$400 – Prob Rules
$400 Answer from Prob Rules
5 4
20
 
15 14 210
$500 – Prob Rules
A box contains 4 red and 2 blue
chips. A chip is drawn at random
and then replaced. A second
chip is then drawn at random.
What is the probability that they
are both the same color?
$500 Answer from H2
P [ ( r  r )  (b  b )]
4 4 2 2
 6 6 6 6

 

16 4 20 5



36 36 36 9
$100 - Tables
Response to Question
Yes
No
Maybe
Sophomores
87
44
34
165
Juniors
88
87
26
201
Seniors
29
39
66
134
204
170
126
500
P  Sophomore  
$100 Answer from Tables
165
500
$200 - Tables
Response to Question
Yes
No
Maybe
Sophomores
87
44
34
165
Juniors
88
87
26
201
Seniors
29
39
66
134
204
170
126
500
P ( Jr  Yes ) 
$200 Answer from Tables
88
500
$300 Question from Tables
Response to Question
Yes
No
Maybe
Sophomores
87
44
34
165
Juniors
88
87
26
201
Seniors
29
39
66
134
204
170
126
500
P  Jr  Sr  
$300 Answer from Tables
335
500
$400 - Tables
Response to Question
Yes
No
Maybe
Sophomores
87
44
34
165
Juniors
88
87
26
201
Seniors
29
39
66
134
204
170
126
500
P  Soph  Maybe  
$400 Answer from Tables
165 126 34


500 500 500
257
500
$500 - Tables
Response to Question
Yes
No
Maybe
Sophomores
87
44
34
165
Juniors
88
87
26
201
Seniors
29
39
66
134
204
170
126
500
Are the events being a
junior and responding
“yes” independent?
$500 Answer from Tables
?
P  Jr | Yes   P( Jr )
88 201

204 500
They are dependent
– not independent!
$100 Question from Mixed Rules
Approximately 44% of children
under 12 have had the chicken pox.
What’s the probability of
randomly choosing three children
and all three have had the chicken
pox?
$100 Answer from Mixed Rules
(.44)(.44)(.44) = 0.085184
$200 - Mixed Rules
The probability that Mary will visit
Walt Disney World is 0.35, the
probability that she will visit Epcot
Center is 0.7. The probability that
she will visit both places is 0.12.
What is the probability that Mary
will visit at least one of the two
places?
$200 Answer from Mixed Rules
.35+.7-.12 = 0.93
$300 – Mixed Rules
A survey was taken among a group of
people. The probability that a person has a
land line phone in his house is 0.93, the
probability that they own a cell phone is 0.71,
and that probability that a person owns both
a land line and a cell phone is 0.66
What is the probability
that a person does not
have a phone?
$300 Answer from Mixed Rules
1 - (0.93+0.71 – 0.66) = 0.02
$400 Question from Mixed Rules
The probability of failing a
certain class is 0.20. What is the
probability that in a group of 4
students from that class, at least
one failed the class?
$400 Answer from H4
1 – P(none failed)
1 – (.8^4)
1-.4096
0.5904
$500 - Mixed Rules
It is estimated that 4% of people who spend time
in the woods will get Lyme disease. Of people
with Lyme disease, the test to determine if you
have it will give a positive reading 97% of the
time. Of people who do not have Lyme disease,
the same test will give a negative rating 92% of
the time. What is the probability that if a person
gets a negative reading, he actually has Lyme
disease?
$500 Answer from Mixed Rules
Positive
Lyme
Negative
0.04(0.03) = 0.0012
Positive
No Lyme
Negative
0.96(0.92) = 0.8832
0.8844
0.0012
P( Lyme | Neg ) 
 0.00136
0.8844
$100 - Misconceptions
In a lotto game, one has to
choose 6 numbers from a
total of 40. Mary has chosen
1,2,3,4,5,6. Ruth has chosen
39, 1, 17, 33, 8, 27. Who has
a greater chance of winning?
$100 Answer from Misconceptions
Neither, both have the
same chance of
winning!
$200 - Misconceptions
When tossing a coin, there are two possible
outcomes: either heads or tails. Ron flipped a coin
three times and in all cases heads came up. Ron
intends to flip the coin again. what is the chance of
getting heads the fourth time?
$200 Answer from H5
1
2
$300 - Misconceptions
In a certain town there are two hospitals, a small one in which
there are, on the average, about 15 births a day and a big
one in which there are, on the average, about 45 births a
day. The likelihood of giving birth to a boy is about 50%. In
the small hospital a record has been kept during the year of
the days in which the total number of boys born was greater
than 9, which represents more than 60% of the total births
in the small hospital. In the big hospital, they have kept a
record during the year of the days in which there were more
than 27 boys born, which represents more than 60% of the
births. In which of the two hospitals were there more such
days or were they equal?
$300 Answer from Misconceptions
Small Hospital
$400 - Misconceptions
When choosing a committee composed of 2 members
from among 10 candidates, the number of
possibilities is (smaller than, equal to, greater
than) then number of possibilities when choosing
a committee of 8 members from among 10
candidates.
$400 Answer from Misconceptions
They are equal:
10 C2
 45
10 C8
 45
$500 Question from H5
Jim and Bill each receive a box containing two white marbles and
two black marbles.
A. Jim extracts a marble from his box and finds out that it is a white
one. Without replacing the first marble, he extracts a second
marble. Is the likelihood that this second marble is also white
(smaller than, equal to, or greater than) the likelihood that it is a
black marble?
B. Bill extracts a marble from his box and puts it aside without
looking at it. He then extracts a second marble and sees
that it is white. Is the likelihood that the first marble he
extracted is white (smaller than, equal to, or greater than) the
likelihood that it is black?
$500 Answer from H5
A. Smaller since P(W|W) = 1/3
and P(B|W) = 2/3
B. Smaller since first draw had to be
out of one white and two black,
probability of white was smaller.
$100 Question from H6
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$100 Answer from H6
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$200 Question from H6
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$200 Answer from H6
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$300 Question from H6
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$300 Answer from H6
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$400 Question from H6
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$400 Answer from H6
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$500 Question from H6
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$500 Answer from H6
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Final Jeopardy
This author wrote, “If one man kills another,
it murder, but if a hundred thousand men kill
another hundred thousand, it is considered an
act of glory!?”
Final Jeopardy Answer
Who is Tolstoy?
(The book is
Kingdom of God)