Probability Stats

Question

A jury has 12 jurors. A vote of at least 10 of 12 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 anyone juror makes the correct decision on a defendant is .80. If the defendant is guilty, what is the probability that the jury makes the correct decision?

Answer 1

≥If the jurors are independent and we can state their behavior as a percentage of the time being correct, the distribution of votes should be binomial. The percentage required is P(10 or more jurors correct)

P(n≥10) = ₁₂C₁₀(.8)¹⁰(.2)² + ₁₂C₁₁(.8)¹¹(.2) + ₁₂C₁₂(.8)¹²

where _nC_k is the combination of n things k at a time or "n choose k"

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