Binomial Problem A jury has 12 jurors A vote of at least 10

Binomial Problem:

A jury has 12 jurors. A vote of at least 10 out 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 .80. If the defendeant is guitly, what is the probability that the jury makes the correct decision?

Solution

Binomial Problem:

A jury has 12 jurors. A vote of at least 10 out 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 .80. If the defendeant is guitly, what is the probability that the jury makes the correct decision?

p=0.80

n=12

P(X=x) = (_nC_x) p^x (1-p)^n-x

P( X >=10) = P(X=10)+ P(X=11)+ P(X=12)

= 0.2835+ 0.2062+ 0.0687

= 0.5584