Unknown user at 19:51, 11 May 2025

2025-05-11T19:51:04Z

← Older revision		Revision as of 19:51, 11 May 2025
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	\|solution=		\|solution=

			This is a classic probability problem where you have to think about a scenario involving two conditions, which means you have to think about <math>A \land B</math>, but also <math>\neg A \land \neg B</math>

	We start by calculating two quantities:		We start by calculating two quantities:

Admin: Admin moved page FMM14 to FMM15

2019-11-22T22:27:29Z

Admin moved page FMM14 to FMM15

← Older revision	Revision as of 22:27, 22 November 2019
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Admin at 21:00, 17 November 2019

2019-11-17T21:00:16Z

← Older revision		Revision as of 21:00, 17 November 2019
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	Ratio = 41.4%		Ratio = 41.4%
			}}

Admin: Created page with "{{FMM |title=Which Color Cab |problem= The psychologists Daniel Kahneman and Amos Tversky used the following example to demonstrate the common failure to evaluate objective p..."

2019-11-17T21:00:07Z

Created page with "{{FMM |title=Which Color Cab |problem= The psychologists Daniel Kahneman and Amos Tversky used the following example to demonstrate the common failure to evaluate objective p..."

New page

{{FMM
|title=Which Color Cab
|problem=

The psychologists Daniel Kahneman and Amos Tversky used the following example to demonstrate the common failure to evaluate objective probabilities.

A cab is involved in a hit-and-run accident at night. Two cab companies, Blue and Green, operate in a city. You are given the following data:

A) 85% of cabs are green, 15% are blue

B) A witness identified the cab as blue. The reliability of the witness under the given conditions is that they correctly identify the color of the cab 80% of the time.

What is the probability that the cab the witness saw is actually blue?

|solution=

We start by calculating two quantities:

1) The probability that the cab's apparent color was correctly identified

2) The probability that the cab's true color was correctly identified

Case 1 is the superset, Case 2 is a subset. By taking the ratio of these two, we get the percent of time that the witness, identifying the cab color as blue, is correct because the cab was truly blue.

Quantity 1:

<pre>
P(cab's apparent color correctly IDed)
= P(cab actually blue) P(blue cab IDed as blue) + P(cab actually green) P(green cab IDed as blue)
= (.15)(.80) + (.85)(.20)
= (.12) + (.17)
= .29
</pre>

Quantity 2:

<pre>
P(cab's true color correctly IDed)
= P(cab actually blue) P(blue cab IDed as blue)
= (.15)(.80)
= .12
</pre>

Ratio of these two quantities is the percent of time the ID of a blue cab is because cab is actually blue:

Ratio = 41.4%

FMM15 - Revision history

Unknown user at 19:51, 11 May 2025

Admin: Admin moved page FMM14 to FMM15

Admin at 21:00, 17 November 2019

Admin: Created page with "{{FMM |title=Which Color Cab |problem= The psychologists Daniel Kahneman and Amos Tversky used the following example to demonstrate the common failure to evaluate objective p..."