jeopardy

Jeopardy

Final Jeopardy

DefinitionsProb Rules

TablesMixed Rules

Mis-

conceptions

$100 $100 $100 $100 $100

$200 $200 $200 $200 $200

$300 $300 $300 $300 $300

$400 $400 $400 $400 $400

$500 $500 $500 $500 $500

$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.


Sample Space

$300 - Definitions

Knowledge of one event having occurred does not affect the probability of the occurrence of the second event.


Independent

$400 - Definitions

An activity or situation in which there is uncertainty concerning which of two or more possible outcomes will result


Chance Experiment

$500 - Definitions

Probability based on the sample space of an event


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 rulesTwo 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

Calculate the probability that neither A nor B wins.

1 1 1

3 5 9, , and respectively

$300 Answer from Prob Rules

P(neither A nor B will win) = 1 – P(either A or B will win)

1 11

3 5

8 71

15 15

$400 – Prob Rules

A bag contains 6 red, 5 blue and 4 yellow marbles. Two marbles are drawn without replacement, find the probability that they are both blue.

$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

4 4 2 2

6 6 6 6

16 4 20 5

36 36 36 9

[ ( ) ( )]P r r b b

$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

SophomoreP

$100 Answer from Tables

165

500

$200 - TablesResponse to Question

Yes No Maybe


Juniors 88 87 26 201

Seniors 29 39 66 134

204 170 126 500

( )P Jr Yes


88

500

$300 Question from TablesResponse to Question

Yes No Maybe


Juniors 88 87 26 201

Seniors 29 39 66 134

204 170 126 500

P Jr Sr


335

500

$400 - Tables


Yes No Maybe


Juniors 88 87 26 201

Seniors 29 39 66 134

204 170 126 500

P Soph Maybe


165 126 34

500 500 500257

500

$500 - Tables


Yes No Maybe


Juniors 88 87 26 201

Seniors 29 39 66 134

204 170 126 500

Are the events being a junior and responding “yes” independent?


88 201

204 500

?

| ( )P Jr Yes P Jr

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 RulesThe 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?


.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?


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-.40960.5904

$500 - Mixed RulesIt 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?


Lyme

No Lyme

Positive

Positive

Negative

Negative

0.04

0.96

0.97

0.03

0.08

0.92

0.04(0.03) = 0.0012

0.96(0.92) = 0.8832

0.8844

0 00120 00136

0 8844

.( | ) .

.P Lyme Neg

$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!


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 - MisconceptionsIn 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?


Small Hospital


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.


They are equal:

10 2

10 8

45

45

C

C

$500 Question from H5Jim 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 H5A. 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 Answer from H6

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$300 Answer from H6

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$400 Answer 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)

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