A three person jury decides by majority vote There are two j

A three- person jury decides by majority vote. There are two jurors each of whom independently has probability p of making the correct decision, and a third juror who flips a coin for each decision. A one- person jury has probability p of making the correct decision. Which jury has the higher probability of making the correct decision?

Solution

probability of making right decision of 3 person jury = p*p+p*0.5+p*0.5 = p²+p

which is greater than probability p of making right decision of one person jury

so three person jury has higher probability of getting the right decision