A three-person jury is to decide whether a defendant is guilty or innocent using

Question

A three-person jury is to decide whether a defendant is guilty or innocent using majority rule (i.e the final verdict is the majority verdict from the jurors). Based on the jury selection responses, the prosecutor estimates that the three jurors will vote for a guilty verdict with probability 0.95, 0.85 and 0.45 respectively. The defense attorney estimates that they will vote for a not-guilty verdict with probability 0.7, 0.7, 0.9. a. What is the prosecutor’s estimate of the likelihood of a guilty verdict? b. What is the defense attorney’s estimate of the likelihood of a not-guilty verdict?

Explanation / Answer

a)prosecutor’s estimate of the likelihood of a guilty verdict =P( two or more will vote of a guilty verdict )

=P(exactly 2 will vote for guilty verdict + all 3 vote for guilty verdict )

=(0.95*0.85*(1-0.45)+0.95*(1-0.85)*0.45+(1-0.95)*0.85*0.45)+(0.95*0.85*0.45)=0.89075

b)defense attorney’s estimate of the likelihood of a not-guilty verdict =P( two or more will vote of a not-guilty verdict )

=P(exactly 2 will vote fornot-guilty verdict + all 3 vote for not-guilty verdict )

=(0.7*0.7*(1-0.9)+0.7*(1-0.7)*0.9+(1-0.7)*0.7*0.9)+0.7*0.7*0.9 =0.868

please revert for any clarification requierd,

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