SOLUTION: 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

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Question 166579: 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 any one juror makes the correct decision on a defendant is 0.88. If the defendant is guilty, what is the probability that the jury makes the correct decision? (Round your answer to 4 decimal places.)
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
a=.88 probability of a correct decision.
b=.12 probability of an incorrect decision.
We need the 1st 3 terms of (a+b)^12
a^12=.88^12=.21567
12a^11b=12*.88^11*.12=.35292
66a^10b^2=66*.88^10*.12^2=.26469
.21567+35292+.26469=.8333 probability that the jury makes the correct decision.
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Ed