Mixing
Change of probablity $60%-40%$, after given information on sample space of $15%$
$begingroup$
Officer A suspects (lefthanded) person P for being guilty of a crime, with percentage $60% -40%$ ($60$:guilty, $40$ not guilty).
After a call from another officer, say B, officer A was informed that it is proved that the crime was commited by a left handed person (where the lefthanded represent $15%$ of the total population in the specific area).
After officer's B information, how has officer's A belief changed about P being guilty?
Attempt. After the information by B, officer's A sample space has changed from all the population to the lefthanded (which is the $15%$ of the total population). But I am not sure how to evaluate our conditional probability $P(A|B)$ ($A$: officer A believes P is guilty, $B$: officer B informs A that the criminal is lefthanded).
Thanks for the help.
probability conditional-probability bayesian bayes-theorem
edited Feb 1 at 3:11
Lee David Chung Lin
4,47841242
asked Jan 30 at 9:37
Nikolaos SkoutNikolaos Skout
2,363619
$endgroup$
add a comment |
$begingroup$
Officer A suspects (lefthanded) person P for being guilty of a crime, with percentage $60% -40%$ ($60$:guilty, $40$ not guilty).
After a call from another officer, say B, officer A was informed that it is proved that the crime was commited by a left handed person (where the lefthanded represent $15%$ of the total population in the specific area).
After officer's B information, how has officer's A belief changed about P being guilty?
Attempt. After the information by B, officer's A sample space has changed from all the population to the lefthanded (which is the $15%$ of the total population). But I am not sure how to evaluate our conditional probability $P(A|B)$ ($A$: officer A believes P is guilty, $B$: officer B informs A that the criminal is lefthanded).
Thanks for the help.
probability conditional-probability bayesian bayes-theorem
edited Feb 1 at 3:11
Lee David Chung Lin
4,47841242
asked Jan 30 at 9:37
Nikolaos SkoutNikolaos Skout
2,363619
$endgroup$
$begingroup$
This [related post] has very similar setting with a key difference in the prior. Are you sure there's no more information on how to interpret the opening statement "Officer A suspects the lefthanded person P for being guilty with $0.6$ probability"?
$endgroup$
– Lee David Chung Lin
Feb 1 at 22:14
add a comment |
$begingroup$
Officer A suspects (lefthanded) person P for being guilty of a crime, with percentage $60% -40%$ ($60$:guilty, $40$ not guilty).
After a call from another officer, say B, officer A was informed that it is proved that the crime was commited by a left handed person (where the lefthanded represent $15%$ of the total population in the specific area).
After officer's B information, how has officer's A belief changed about P being guilty?
Attempt. After the information by B, officer's A sample space has changed from all the population to the lefthanded (which is the $15%$ of the total population). But I am not sure how to evaluate our conditional probability $P(A|B)$ ($A$: officer A believes P is guilty, $B$: officer B informs A that the criminal is lefthanded).
Thanks for the help.
probability conditional-probability bayesian bayes-theorem
edited Feb 1 at 3:11
Lee David Chung Lin
4,47841242
asked Jan 30 at 9:37
Nikolaos SkoutNikolaos Skout
2,363619
$endgroup$
Officer A suspects (lefthanded) person P for being guilty of a crime, with percentage $60% -40%$ ($60$:guilty, $40$ not guilty).
After a call from another officer, say B, officer A was informed that it is proved that the crime was commited by a left handed person (where the lefthanded represent $15%$ of the total population in the specific area).
After officer's B information, how has officer's A belief changed about P being guilty?
Attempt. After the information by B, officer's A sample space has changed from all the population to the lefthanded (which is the $15%$ of the total population). But I am not sure how to evaluate our conditional probability $P(A|B)$ ($A$: officer A believes P is guilty, $B$: officer B informs A that the criminal is lefthanded).
Thanks for the help.
probability conditional-probability bayesian bayes-theorem
probability conditional-probability bayesian bayes-theorem
edited Feb 1 at 3:11
Lee David Chung Lin
4,47841242
asked Jan 30 at 9:37
Nikolaos SkoutNikolaos Skout
2,363619
edited Feb 1 at 3:11
Lee David Chung Lin
4,47841242
asked Jan 30 at 9:37
Nikolaos SkoutNikolaos Skout
2,363619
edited Feb 1 at 3:11
Lee David Chung Lin
4,47841242
edited Feb 1 at 3:11
Lee David Chung Lin
4,47841242
edited Feb 1 at 3:11
Lee David Chung Lin
4,47841242
4,47841242
asked Jan 30 at 9:37
Nikolaos SkoutNikolaos Skout
2,363619
asked Jan 30 at 9:37
Nikolaos SkoutNikolaos Skout
2,363619
asked Jan 30 at 9:37
Nikolaos SkoutNikolaos Skout
2,363619
2,363619
$begingroup$
This [related post] has very similar setting with a key difference in the prior. Are you sure there's no more information on how to interpret the opening statement "Officer A suspects the lefthanded person P for being guilty with $0.6$ probability"?
$endgroup$
– Lee David Chung Lin
Feb 1 at 22:14
add a comment |
$begingroup$
This [related post] has very similar setting with a key difference in the prior. Are you sure there's no more information on how to interpret the opening statement "Officer A suspects the lefthanded person P for being guilty with $0.6$ probability"?
$endgroup$
– Lee David Chung Lin
Feb 1 at 22:14
$begingroup$
This [related post] has very similar setting with a key difference in the prior. Are you sure there's no more information on how to interpret the opening statement "Officer A suspects the lefthanded person P for being guilty with $0.6$ probability"?
$endgroup$
– Lee David Chung Lin
Feb 1 at 22:14
$begingroup$
This [related post] has very similar setting with a key difference in the prior. Are you sure there's no more information on how to interpret the opening statement "Officer A suspects the lefthanded person P for being guilty with $0.6$ probability"?
$endgroup$
– Lee David Chung Lin
Feb 1 at 22:14
add a comment |
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$begingroup$
This [related post] has very similar setting with a key difference in the prior. Are you sure there's no more information on how to interpret the opening statement "Officer A suspects the lefthanded person P for being guilty with $0.6$ probability"?
$endgroup$
– Lee David Chung Lin
Feb 1 at 22:14