please show the process of how to fill out the table and answer questions Is bei

Question

please show the process of how to fill out the table and answer questions

Is being in A independent of being in B? Ex: In a Jury trial, suppose the probability the defendant is convicted given guilt is 95% and the probability the defendant is acquitted given innocence is 97%. Suppose that 80% of all defendants are truly guilty. Draw a tree diagram. What is the probability a defendant is acquitted of a crime? a) 0.97 b) 0.198 c0.766 d) 0.234 e) 0.80 Answer: What is the probability that a defendant is convicted of a crime? Answer: What is the probability that a defendant is cither guilty or convicted of a crime? a) 0.80 b) 0.766 c) 0.806 d) 0.76 c) 0.198 Answer Given that the defendant is convicted, find the probability be or she was actually innocent Answer

Explanation / Answer

1) probability that defendent is acquitted of a crime =P(guilty and acquitted +not guilty and acquitted)

=0.8*0.05+0.2*0.97 =0.234

therefore option D is correct

2) probability that defendent is convicted =1-P(acquitted) =1-0.234 =0.766

option B is correct

3)given defendent convicted probability of innocent =P(innocent and convicted)/P(convicted)

=0.2*0.03/0.766=0.0078 ~ 0.008

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