Question

A jury has 17 jurors. A vote of at least 15 of 17 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 0.870. If the defendant is guilty, what is the probability that the jury makes the correct decision?

Answer 1

what is the % of 15 out of 17

Answer 2

it is 88.2%

Answer 3

it would b high very high because the % is very high

Answer 4

There are 3 possible outcomes in the voting of the jury.
1. 15 guilty votes
2.16 guilty votes
3. 17 guilty votes
The probability of a correct decision in each outcome is found as follows:
\[P(correct\ with\ 15\ guilty\ votes)=(0.87)^{15}\]
\[P(correct\ with\ 16\ votes)=(0.87)^{16}\]
\[P(correct\ with\ 17\ votes)=(0.87)^{17}\]
The three outcome events are mutually exclusive. Therefore the probability that the jury makes the correct decision is the sum of the 3 probabilities.

Answer 5

so u add those probabilities?

Answer 6

Yes, first you calculate each of the three values of probability. Then you add the three values together. The results are interesting.

Answer 7

okay the answer that i have recieved is 0.325261251

Answer 8

Your answer is correct. Good work :)
You should round off the answer to, say, P(correct decision) = 0.325