FMM8 - Revision history

Admin at 21:28, 23 January 2020

2020-01-23T21:28:24Z

← Older revision		Revision as of 21:28, 23 January 2020
Line 11:		Line 11:
	\|solution=		\|solution=

	The probability of a 3-person jury making a correct decision is the union of two situations ~~(here, Juror~~ 1 and ~~2 have probability P of~~ being ~~right~~, ~~while Juror~~ 3 ~~has a 50% probability of~~ being ~~right)~~:		The probability of a 3-person jury making a correct decision is the union of two situations: Jurors 1 and 3 being correct, or Jurors 2 and 3 being correct:

	<pre>		<pre>
	P_{3 correct} = ( P_{juror 1 correct} and P_{juror 3 correct} ) or (P_{juror 2 correct} and P_{juror 3 correct})		P_{correct verdict} = ( P_{juror 1 correct} and P_{juror 3 correct} ) or (P_{juror 2 correct} and P_{juror 3 correct})
	</pre>		</pre>

	~~Now we know P_{juror~~ 3 ~~correct} is 0~~.5, we know that "and" translates to multiplication~~, we~~ know that "or" translates to addition~~, so~~:		Juror 1 and 2 have probability P of being right, while Juror 3 has a 50% probability of being right. Furthermore, we know that "and" translates to multiplication of probabilities. We also know that "or" translates to addition of probabilities. The above expression becomes:

	<pre>		<pre>

Admin at 22:20, 16 November 2019

2019-11-16T22:20:39Z

← Older revision		Revision as of 22:20, 16 November 2019
Line 13:		Line 13:
	The probability of a 3-person jury making a correct decision is the union of two situations (here, Juror 1 and 2 have probability P of being right, while Juror 3 has a 50% probability of being right):		The probability of a 3-person jury making a correct decision is the union of two situations (here, Juror 1 and 2 have probability P of being right, while Juror 3 has a 50% probability of being right):

			<pre>
	P_{3 correct} = ( P_{juror 1 correct} and P_{juror 3 correct} ) or (P_{juror 2 correct} and P_{juror 3 correct})		P_{3 correct} = ( P_{juror 1 correct} and P_{juror 3 correct} ) or (P_{juror 2 correct} and P_{juror 3 correct})
			</pre>

	Now we know P_{juror 3 correct} is 0.5, we know that "and" translates to multiplication, we know that "or" translates to addition, so:		Now we know P_{juror 3 correct} is 0.5, we know that "and" translates to multiplication, we know that "or" translates to addition, so:

			<pre>
	P_{3 correct} = 0.5P + 0.5P = P		P_{3 correct} = 0.5P + 0.5P = P
			</pre>

	Meanwhile, the 1 person jury has a probability of making a correct decision of:		Meanwhile, the 1 person jury has a probability of making a correct decision of:

			<pre>
	P_{1 correct} = P		P_{1 correct} = P
			</pre>

	From this, we can see that the two juries have an equal probability of being correct.		From this, we can see that the two juries have an equal probability of being correct.

	}}		}}

Admin: Created page with "{{FMM |title=The Flippant Juror |problem= A 3-person jury has 2 members, each of whom has an independent probability P of making a correct decision. The third juror flips a c..."

2019-11-16T22:19:58Z

Created page with "{{FMM |title=The Flippant Juror |problem= A 3-person jury has 2 members, each of whom has an independent probability P of making a correct decision. The third juror flips a c..."

New page

{{FMM
|title=The Flippant Juror
|problem=

A 3-person jury has 2 members, each of whom has an independent probability P of making a correct decision. The third juror flips a coin. (Majority rules.)

A 1-person jury has 1 member who has a probability P of making the correct decision.

Which jury has a better probability of making the correct decision?

|solution=

The probability of a 3-person jury making a correct decision is the union of two situations (here, Juror 1 and 2 have probability P of being right, while Juror 3 has a 50% probability of being right):

P_{3 correct} = ( P_{juror 1 correct} and P_{juror 3 correct} ) or (P_{juror 2 correct} and P_{juror 3 correct})

Now we know P_{juror 3 correct} is 0.5, we know that "and" translates to multiplication, we know that "or" translates to addition, so:

P_{3 correct} = 0.5*P + 0.5*P = P

Meanwhile, the 1 person jury has a probability of making a correct decision of:

P_{1 correct} = P

From this, we can see that the two juries have an equal probability of being correct.

}}