Mark is on trial for a bank robbery. He has no prior record, and is generally co

Question

Mark is on trial for a bank robbery. He has no prior record, and is generally considered an upstanding member of the community. However, Sam says that she witnessed Mark dashing out of the bank after the robbery, carrying a bag of money. Sam testifies in court, saying that she is very confident that it was Mark who robbed the bank.

The prior probability that Mark committed the crime is 1/100. The probability that Sam correctly identifies people is 90/100. What is the probability that Mark committed the crime, given that Sam said that it was Mark who committed the crime? Show full work

Explanation / Answer

probability that Sam identified Mark as Robber =P( mark commited and Sam identified+Mark has not commited and Sam identified) =(1/100)*(90/100)+(99/100)*(10/100)=0.108

hence  probability that Mark committed the crime, given that Sam said that it was Mark who committed the crime

=P(mark commited and Sam identified)/P(Sam identified) =(1/100)*(90/100)/0.108=0.0833

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