exercise:84e5b5b6bf: Difference between revisions
(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Probability theory was used in a famous court case: ''People v. Collins.''<ref group="Notes" >M. W. Gray, “Statistics and the Law,” ''Mathematics Magazine,'' vol. 56 (1983), pp. 67--81.</ref> In this case a purse was snatched from an elderly...") |
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Probability theory was used in a famous court case: ''People v. Collins.''<ref group="Notes" >M. W. Gray, “Statistics and the Law,” ''Mathematics Magazine,'' vol. 56 (1983), pp. 67--81.</ref> In this case a purse was snatched from an elderly person in a Los Angeles suburb. A couple seen running from the scene were described as a black man with a beard and a | |||
mustache and a blond girl with hair in a ponytail. Witnesses said they drove off in a partly yellow car. Malcolm and Janet Collins were arrested. He was black and though clean shaven when arrested had evidence of recently having had a beard and a mustache. She was blond and usually wore her hair in a ponytail. They drove a partly yellow Lincoln. The prosecution called a professor of mathematics as a witness who suggested that a conservative set of probabilities for the characteristics noted by the witnesses would be as shown in [[guide:448d2aa013#table 4.4 |Table]]. | |||
case: ''People v. Collins.''<ref group="Notes" >M. W. | |||
Gray, “Statistics and the Law,” ''Mathematics Magazine,'' vol. 56 (1983), pp. 67--81.</ref> In | |||
this case a purse was snatched from an elderly person in a Los Angeles suburb. A couple seen | |||
running from the scene were described as a black man with a beard and a | |||
mustache and a blond girl with hair in a ponytail. Witnesses said | |||
they drove off in a partly yellow car. Malcolm and Janet Collins were arrested. He was black and | |||
though clean shaven when arrested had evidence of recently having had a beard | |||
and a mustache. She was blond and usually wore her hair in a ponytail. They | |||
drove a partly yellow Lincoln. The prosecution called a professor of mathematics | |||
as a witness who suggested that a conservative set of probabilities for the | |||
characteristics noted by the witnesses would be as shown in [[guide:448d2aa013#table 4.4 |Table]]. | |||
<span id="table 4.4"/> | <span id="table 4.4"/> | ||
{|class="table" | {|class="table" | ||
|+ Collins case probabilities. | |+ Collins case probabilities. | ||
|- | |- | ||
| | |man with mustache || 1/4 | ||
|- | |||
|girl with blond hair || 1/3 | |||
|- | |||
| girl with ponytail ||1/10 | |||
|- | |||
|black man with beard || 1/10 | |||
|- | |||
|interracial couple in a car || 1/1000 | |||
|- | |||
|| partly yellow car || 1/10 | |||
|} | |} | ||
The prosecution then argued that the probability that all of these characteristics are met by a randomly chosen couple is the product of the | |||
The prosecution then argued that the probability that all of these | probabilities or 1/12,00,00, which is very small. He claimed this was proof beyond a reasonable doubt that the defendants were guilty. The jury agreed | ||
characteristics are met by a randomly chosen couple is the product of the | and handed down a verdict of guilty of second-degree robbery. If you were the lawyer for the Collins couple how would you have countered the | ||
probabilities or 1/12,00,00, which is very small. He claimed this was proof | above argument? (The appeal of this case is discussed in [[exercise:65ab35f324|Exercise]]). | ||
beyond a reasonable doubt that the defendants were guilty. The jury agreed | |||
and handed down a verdict of guilty of second-degree robbery. | |||
If you were the lawyer for the Collins couple how would you have countered the | |||
above argument? (The appeal of this case is discussed in | |||
'''Notes''' | '''Notes''' | ||
{{Reflist|group=Notes}} | {{Reflist|group=Notes}} | ||
Latest revision as of 01:00, 13 June 2024
Probability theory was used in a famous court case: People v. Collins.[Notes 1] In this case a purse was snatched from an elderly person in a Los Angeles suburb. A couple seen running from the scene were described as a black man with a beard and a mustache and a blond girl with hair in a ponytail. Witnesses said they drove off in a partly yellow car. Malcolm and Janet Collins were arrested. He was black and though clean shaven when arrested had evidence of recently having had a beard and a mustache. She was blond and usually wore her hair in a ponytail. They drove a partly yellow Lincoln. The prosecution called a professor of mathematics as a witness who suggested that a conservative set of probabilities for the characteristics noted by the witnesses would be as shown in Table.
| man with mustache | 1/4 |
| girl with blond hair | 1/3 |
| girl with ponytail | 1/10 |
| black man with beard | 1/10 |
| interracial couple in a car | 1/1000 |
| partly yellow car | 1/10 |
The prosecution then argued that the probability that all of these characteristics are met by a randomly chosen couple is the product of the probabilities or 1/12,00,00, which is very small. He claimed this was proof beyond a reasonable doubt that the defendants were guilty. The jury agreed and handed down a verdict of guilty of second-degree robbery. If you were the lawyer for the Collins couple how would you have countered the above argument? (The appeal of this case is discussed in Exercise).
Notes