Question

IN US criminal trials, about 60% of all defendants are found guilty

a)if you were to observe 25 criminal trails, what is the expected number of guilty verdicts?
b) how many trials would you need to observe in order to 96% certain of seeing a guilty verdict?

Answer 1

for a) take 60% of 25. 60% = 60/100. so the answer is?

Answer 2

so part a) is just a matter of applying the percentage
so we are told that 60% of all defendants are found guilty
then if we observe 25 trials
60% of the 25 would be expected to be found guilty.
So we just have to find 60% of 25. Agreed? @ciluvu06

Answer 3

its should be 15
so for part a, the answer would be we would expect 15 out of the 25 to be found guilty

Answer 4

and part B?

Answer 5

b) At a trial the probability of a 'not guilty' verdict is 1 - 0.6 = 0.4 (assuming there is not a mistrial or hung jury).
The probability of 2 not guilty verdicts in successive trials is 0.4 * 0.4 = 0.16.
The probability of 3 successive 'not guilty' verdicts is (0.4)^3 = 0.064.
The probability of 4 successive 'not guilty' verdicts is (0.4)^4 = 0.0256.
Therefore after 4 successive trials the probability of one or more guilty verdicts is:
1.0000 - 0.0256 = 0.97. So 4 trials are needed to be 97% certain of seeing a guilty verdict.

Answer 6

@kropot72 thank you that was very helpful!

Answer 7

You're welcome :)