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OfflineKickleM
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Some cognition stuff * 1
    #28214047 - 03/04/23 12:04 PM (10 months, 20 days ago)

A. A cab was involved in a hit-and-run accident. Two cab companies serve the city: the Green, which operates 85% of the cabs, and the Blue, which operates the remaining 15%. A witness identifies the hit-and-run cab as Blue. When the court tests the reliability of the witness under circumstances similar to those on the night of the accident, he correctly identifies the color of the cab 80% of the time and misidentifies it 20% of the time. What is the probability that the cab involved in the accident was Blue, as the witness stated?
Odds
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Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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OfflineKickleM
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Re: Some cognition stuff [Re: Kickle]
    #28214051 - 03/04/23 12:06 PM (10 months, 20 days ago)

B. You've reserved a seat for a Broadway play for which the ticket price is $40. As you enter the theater to buy your ticket, you discover you've lost $40 from your pocket. Would you still buy the ticket? (Assume you still have enough left to do so.)
Yes/no
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Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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OfflineKickleM
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Re: Some cognition stuff [Re: Kickle]
    #28214054 - 03/04/23 12:08 PM (10 months, 20 days ago)

C. Linda is 31, single, outspoken, and very bright. She majored in philosophy in college. As a student, she was deeply concerned with discrimination and other social issues, and participated in anti-nuclear demonstrations. Which statement is more likely?
Linda
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Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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OfflineKickleM
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Re: Some cognition stuff [Re: Kickle]
    #28214056 - 03/04/23 12:09 PM (10 months, 20 days ago)

D. Threatened by a superior force, the general faces a dilemma. Her intelligence officers say her soldiers will be caught in an ambush in which 600 of them will die unless she leads them to safety by one of two available routes. If she takes the first route, 200 of her soldiers will be saved. If she takes the second, there's a one-third chance that 600 soldiers will be saved and a two-thirds chance that none will be saved. Which route should she take?
Route
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Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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OfflineKickleM
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Re: Some cognition stuff [Re: Kickle] * 1
    #28214067 - 03/04/23 12:13 PM (10 months, 20 days ago)

E. A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. Although the overall proportion of boys is about 50%, that actual proportion at either hospital may be greater or less that 50% on any given day. At the end of the year, which hospital will have the greater number of days on which more than 60% of the babies born were boys?
Hospital
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Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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OfflineKickleM
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Re: Some cognition stuff [Re: Kickle] * 1
    #28214095 - 03/04/23 12:30 PM (10 months, 20 days ago)

After thoughts:

these are commonly used cognition tests for humans around heuristic judgements. They are designed to showcase how during mentally challenging situations we often rely on mental shortcuts. A fun after test is to compare how you approached/answered these questions with how ChatGPT approaches the questions.

Can we learn anything by looking at ChatGPT in regards to heuristics? Will we learn about biases? Does computational power have limits which will result in heuristics emerging? Or is it always giving the purely logical answer?


--------------------
Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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InvisibleRahz
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Re: Some cognition stuff [Re: Kickle]
    #28214367 - 03/04/23 03:25 PM (10 months, 19 days ago)

How many troops does the general have total, 600?


--------------------
rahz

comfort pleasure power love truth awareness peace


"You’re not looking close enough if you can only see yourself in people who look like you." —Ayishat Akanbi


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OfflineKickleM
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Re: Some cognition stuff [Re: Rahz]
    #28214469 - 03/04/23 04:32 PM (10 months, 19 days ago)

Up to you to decide :thumbup:


--------------------
Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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Invisiblesudly
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Registered: 01/05/15
Posts: 10,797
Re: Some cognition stuff [Re: Kickle]
    #28215123 - 03/04/23 11:12 PM (10 months, 19 days ago)

Quote:

Kickle said:
A. A cab was involved in a hit-and-run accident. Two cab companies serve the city: the Green, which operates 85% of the cabs, and the Blue, which operates the remaining 15%. A witness identifies the hit-and-run cab as Blue. When the court tests the reliability of the witness under circumstances similar to those on the night of the accident, he correctly identifies the color of the cab 80% of the time and misidentifies it 20% of the time. What is the probability that the cab involved in the accident was Blue, as the witness stated?




The witness is unreliable.


--------------------
I am whatever Darwin needs me to be.



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Invisiblesudly
Darwin's stagger

Registered: 01/05/15
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Re: Some cognition stuff [Re: Kickle]
    #28215125 - 03/04/23 11:13 PM (10 months, 19 days ago)

Quote:

Kickle said:
B. You've reserved a seat for a Broadway play for which the ticket price is $40. As you enter the theater to buy your ticket, you discover you've lost $40 from your pocket. Would you still buy the ticket? (Assume you still have enough left to do so.)




A reservation usually required payment already.


--------------------
I am whatever Darwin needs me to be.



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Invisiblesudly
Darwin's stagger

Registered: 01/05/15
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Re: Some cognition stuff [Re: Kickle]
    #28215127 - 03/04/23 11:14 PM (10 months, 19 days ago)

Quote:

Kickle said:
C. Linda is 31, single, outspoken, and very bright. She majored in philosophy in college. As a student, she was deeply concerned with discrimination and other social issues, and participated in anti-nuclear demonstrations. Which statement is more likely?




Jobs in philosophy are difficult to come by, she could be a barrista for all we know.


--------------------
I am whatever Darwin needs me to be.



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Invisiblesudly
Darwin's stagger

Registered: 01/05/15
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Re: Some cognition stuff [Re: Kickle]
    #28215129 - 03/04/23 11:16 PM (10 months, 19 days ago)

Quote:

Kickle said:
D. Threatened by a superior force, the general faces a dilemma. Her intelligence officers say her soldiers will be caught in an ambush in which 600 of them will die unless she leads them to safety by one of two available routes. If she takes the first route, 200 of her soldiers will be saved. If she takes the second, there's a one-third chance that 600 soldiers will be saved and a two-thirds chance that none will be saved. Which route should she take?




How many of the enemy will die? What are the goals of the operation? If she doesn't choose the first path, perhaps more soldiers or civilians will die afterwards.


--------------------
I am whatever Darwin needs me to be.



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Invisiblesudly
Darwin's stagger

Registered: 01/05/15
Posts: 10,797
Re: Some cognition stuff [Re: Kickle]
    #28215132 - 03/04/23 11:22 PM (10 months, 19 days ago)

Quote:

Kickle said:
E. A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. Although the overall proportion of boys is about 50%, that actual proportion at either hospital may be greater or less that 50% on any given day. At the end of the year, which hospital will have the greater number of days on which more that 60% of the babies born were boys?




If both the large and small hospitals can have more or less boys born on any given day, it's hard to say that any of them would reach 60% baby boys on any given day.


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I am whatever Darwin needs me to be.



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Invisibleredgreenvines
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Re: Some cognition stuff [Re: sudly]
    #28215282 - 03/05/23 03:00 AM (10 months, 19 days ago)

granted the scenarios are not optimally informed.
Much of life is managed reflexively or intuitively.
Some even declare we decide pre-cognitively, certainly without much mathematical  computation, though we would like to imagine we think logically and sequentially.

I felt all the questions lacked clarity, but so does much of life.


--------------------
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OfflineKickleM
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Re: Some cognition stuff [Re: redgreenvines]
    #28215550 - 03/05/23 09:19 AM (10 months, 19 days ago)

F. An urn is filled with with white balls and black balls. You know that two-thirds of the balls are of one color and one-third are of the other, but you don't know which color predominates. One blindfolded person plunges a hand into the urn and comes up with three black balls and one white ball. Another uses both hands and comes up with 14 black balls and ten white balls. Both samples suggest that black balls are more numerous. But which sample produces the more convincing evidence?
Sample
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Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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OfflineKickleM
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Re: Some cognition stuff [Re: Kickle]
    #28215554 - 03/05/23 09:20 AM (10 months, 19 days ago)

G. Choose between
Choice
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Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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OfflineKickleM
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Re: Some cognition stuff [Re: Kickle]
    #28215555 - 03/05/23 09:22 AM (10 months, 19 days ago)

H. You've decided to see a Broadway play and have bought a $40 ticket. As you enter the theater, you realize you've lost your ticket. you can't remember the seat number so you can't prove to the management that you bought a ticket. Would you spend $40 for a new ticket?
Yes/no
You may choose only one


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Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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OfflineKickleM
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Re: Some cognition stuff [Re: Kickle]
    #28215557 - 03/05/23 09:24 AM (10 months, 19 days ago)

I. Threatened by a superior force, the general has to choose between two escape routes. Her aides tell her that if she takes the first, 400 soldiers will die. If she takes the second, there's a one-third chance that no soldier will die, and a two-thirds chance that 600 soldiers will die. Which route should she take?
Route
You may choose only one


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Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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OfflineKickleM
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Re: Some cognition stuff [Re: Kickle]
    #28215558 - 03/05/23 09:25 AM (10 months, 19 days ago)

J. Choose between
Choice
You may choose only one


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Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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OfflineKickleM
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Re: Some cognition stuff [Re: Kickle]
    #28215566 - 03/05/23 09:35 AM (10 months, 19 days ago)

After thoughts:
chatGPT on F:

To determine which sample produces more convincing evidence, we can use statistical inference to calculate the likelihood of each sample occurring under the assumption that black balls are more numerous in the urn.

Let B be the number of black balls in the urn, and W be the number of white balls. We know that:

B + W = total number of balls in the urn

And:

B / (B + W) = 2/3 (since two-thirds of the balls are of one color)

Solving for B and W, we get:

B = 2/3 (B + W)

W = 1/3 (B + W)

So, the ratio of black to white balls in the urn is:

B/W = (2/3)/(1/3) = 2

Therefore, there are twice as many black balls as white balls, or vice versa.

Now, let's consider the first sample of three black balls and one white ball. If black balls are more numerous, then the probability of selecting three black balls and one white ball is:

P(3 black, 1 white | black predominates) = (B/B+W) * (B-1/B+W-1) * (B-2/B+W-2) * (W/B+W-3)

Plugging in B/W = 2, we get:

P(3 black, 1 white | black predominates) = (2/3) * (1/2) * (1/3) * (1/4) = 1/18

On the other hand, if white balls are more numerous, then the probability of selecting three black balls and one white ball is:

P(3 black, 1 white | white predominates) = (W/B+W) * (W-1/B+W-1) * (W-2/B+W-2) * (B/B+W-3)

Plugging in B/W = 1/2, we get:

P(3 black, 1 white | white predominates) = (1/3) * (2/5) * (3/7) * (1/2) = 6/315

To compare the strength of evidence, we can calculate the likelihood ratio of the two scenarios:

LR = P(3 black, 1 white | black predominates) / P(3 black, 1 white | white predominates) = (1/18) / (6/315) = 35/2

This means that the first sample is 17.5 times more likely to occur if black balls are more numerous than if white balls are more numerous.

Now, let's consider the second sample of 14 black balls and 10 white balls. If black balls are more numerous, then the probability of selecting 14 black balls and 10 white balls is:

P(14 black, 10 white | black predominates) = (B/B+W)^14 * (W/B+W)^10

Plugging in B/W = 2, we get:

P(14 black, 10 white | black predominates) = (2/3)^14 * (1/3)^10 = 0.000057

On the other hand, if white balls are more numerous, then the probability of selecting 14 black balls and 10 white balls is:

P(14 black, 10 white | white predominates) = (W/B+W)^14 * (B/B+W)^10

Plugging in B/W = 1/2, we get:

P(14 black, 10 white | white predominates) = (1/3)^14 * (2/3)^10 = 0.000003

To compare the strength of evidence, we can calculate the likelihood ratio of the two scenarios:

LR = P(14 black, 10 white | black predominates) / P(14 black, 10 white | white predominates) = 0.000057 / 0.000003 = 19

This means that the second sample is 19 times more likely to occur if black balls are more numerous than if white balls are more numerous.

Comparing the likelihood ratios of the two samples, we see that the second sample produces stronger evidence in favor of black balls being more numerous in the urn. The likelihood ratio of the second sample is 19, whereas the likelihood ratio of the first sample is 17.5 times less than that, at 35/2.

Therefore, we can conclude that the second sample produces the more convincing evidence that black balls are more numerous in the urn. However, it is worth noting that both samples are consistent with the hypothesis that black balls are more numerous, and more data would be needed to make a definitive conclusion.


--------------------
Why shouldn't the truth be stranger than fiction?
Fiction, after all, has to make sense. -- Mark Twain


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