Hey guys, I need help with the following question:
In a military trial it takes at least 10 votes from a 12-member jury to convict a defendant. Suppose that the probability that a juror votes a guilty person innocent is 20 percent whereas the probability that a juror votes an innocent person guilty is 10 percent. Assume that each juror acts independently and that 65 percent of defendants are guilty. Calculate the proportion of defendants that are convicted?
Here is what I have done so far:
I found the probability that a juror will decide on guilty (may it be an innocent convict or guilty convict) as follows:
P(guilty) = P(innocent/guilty) + P(guilty/guilty) = 0.1 + 0.8 = 0.9
Then using the Binomial Distribution formula, with n=12, x=10,11,12, and pie=0.9, i found the probabilities of the three x values:
p(10) = 0.230
p(11) = 0.377
p(12) = 0.282
What do I do now?
In a military trial it takes at least 10 votes from a 12-member jury to convict a defendant. Suppose that the probability that a juror votes a guilty person innocent is 20 percent whereas the probability that a juror votes an innocent person guilty is 10 percent. Assume that each juror acts independently and that 65 percent of defendants are guilty. Calculate the proportion of defendants that are convicted?
Here is what I have done so far:
I found the probability that a juror will decide on guilty (may it be an innocent convict or guilty convict) as follows:
P(guilty) = P(innocent/guilty) + P(guilty/guilty) = 0.1 + 0.8 = 0.9
Then using the Binomial Distribution formula, with n=12, x=10,11,12, and pie=0.9, i found the probabilities of the three x values:
p(10) = 0.230
p(11) = 0.377
p(12) = 0.282
What do I do now?