The Prosecutor's Fallacy

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Monday, March 1. 2010

The Prosecutor's Fallacy

Prof. Lindzen, in his talk at Fermilab which we posted yesterday, refers to the Prosecutor's Fallacy (aka Defender's Fallacy), which refers to a strategy of counting on a jury's inability to understand statistics, and specifically conditional probability.

Conditional probability is about the amount of linkage in events.

The simpest case: Given a red, green and blue marble in a bag, what are the odds of drawing a blue one after drawing a red one?

See the sad case of Sally Clark, who fell victim to the fallacy.

Posted by The Barrister in Fallacies and Logic, Our Essays at 16:14 | Comments (6) | Trackbacks (0)

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Oscar Wilde said losing one parent is a tragedy - losing two is carelessness

#1 Pat Moffitt on 2010-03-01 16:17 (Reply)

"what are the odds of drawing a blue one after drawing a red one?"

Perhaps you might rephrase as "what are the odds of the occurrence of the compound event consisting of first drawing a red one and then drawing a red one?"

Because the answer to your question is 50%, as every card player knows, whereas the answer you wanted was .33333...*.5.

#2 Fred Z on 2010-03-01 17:21 (Reply)

I thought I was clear about red/blue. Maybe not.

#2.1 theb on 2010-03-01 17:30 (Reply)

Once the red marble has been drawn, the question becomes:
Given a green and blue marble in a bag, what are the odds of drawing a blue one ?

#2.1.1 DOuglas2 on 2010-03-01 22:21 (Reply)

No - while that is a practical look at it, statistically you are talking about a compound statistical event - meaning that you have to consider the whole and not the part.

It's like the old saw about flipping a coin and getting 50/50 odd of heads or tails. Not so. Statistically, one or the other will appear 53% of the time, the other 47% of the time. That's what gamblers, good ones anyway, know and use to their advantage.

#2.1.1.1 Tom Francis on 2010-03-02 15:22 (Reply)

(and Tom)
>you have to consider the whole and not the part

As stated, it appears to me that your are prohibited from considering the compound probability:

what are the odds of drawing a blue one after drawing a red one

After you draw marbles until a red one is produced (per the statement) you want to know what the chance now is of pulling the blue one out.

If the answer is 1/6, then the blue one must be much smaller than the red one!

#2.2 CentralCoastRick on 2010-03-02 19:07 (Reply)

Perhaps the question is not specific enough, but given what it is, there are only 3 marbles, therefore there are 6 possible combinations on removal of the marbles.
RBG
RGB
BGR
BRG
GRB
GBR
From these, it is clear that there are 3 occurrences of B after R, though one of them has G in between. Since the question doesn't specifically state "immediately" after then the answer must be 3 and that is 50%.

#3 BargHumer on 2010-03-05 04:50 (Reply)

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Monday, March 1. 2010

The Prosecutor's Fallacy