Question

A jury has 17 jurors. A vote of at least 15 of 17 for “guilty” is necessary for a defendant to be convicted of a crime. Assume that each juror acts independently of the others and that the probability that any one juror makes the correct decision on a defendant is 0.870. If the defendant is guilty, what is the probability that the jury makes the correct decision?

Answer 1

\[\sum_{k=15}^{17} \binom{17}{k}(0.870)^k(1-0.870)^{17-k}\]