Question

In Japanese criminal trials, about 95% of the defendants are found guilty. In the United States, about 60% of the defendants are found guilty in criminal trials. Suppose you are a news reporter following twelve criminal trials.

(a) If the trials were in Japan, what is the probability that all the defendants would be found guilty? What is this probability if the trials were in the United States?
(b) Of the ten trials, what is the expected number of guilty verdicts in Japan? What is the expected number in the United Sates? What is the standard deviation in each case?

Answer 1

a) Japan =0.599

US= 0.006

b) Japan

Variance= 0.475

Standard Deviation =0.69

USA

Variance =2.4

Standard Deviation= 1.55

Explanation:

A represents the number of defendants found guilty in Japan in 10 trials

B represents the number of defendants found guilty in US in 10 trials

A represents a binomial function such that n=10,p=0.95 and B represents a binomial function such that n=10,p=0.60

a) Japan: P(A=10)=0.95^10=0.599

US: P(B=10)=0.60^10=0.006

b) Japan:

Expected number of guilty verdicts in 10 trials in Japan = np=10*0.95=9.5

Variance: Var(A) = np(1-p) = 10*0.95*(1-0.95) = 0.475

Standard Deviation = sd(A)=√0.475=0.69

US:

Expected number of guilty verdicts in 10 trials in USA = np=10*0.60=6

Variance: Var(B)=np(1-p)=10*0.6*0.4=2.4

Standard Deviation sd(B)=√2.4=1.55