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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 any one juror makes the correct decision regarding a defendant is.70. If the defendant is guilty, what is the probability that the jury makes the correct decision?

Answer 1

Chad, this solution is incorrect. 

 

You should use binomial probabilities to solve this problem.

Answer 2

Given there are 12 jurors each independent of each other we know there are 12 trials. The probability of "success" is given at 0.70 and at least 10 must be successful to make the correct decision. Thus P(X>= 10) = ? Alternatively you could solve this by adding the cumulative probabilities of P(X=10) + P(X=11) + P(X=12) and it gives approximately the same answer.