Innocent until proven guilty? in japanese criminal trials, about 95% of the defendants

1

Step-by-step explanation:

This situation can be modeled with the Binomial Distribution which gives the probability of an event that occurs exactly k times out of n, and is given by

where  

= combination of n elements taken k at a time.

p = probability that the event (“success”) occurs once

q = 1-p

In this case, the event “success” is finding a defendant guilty (in Japan) with probability 95% = 0.95 (9.5 out of 10) and n=10 criminal trials randomly chosen.

“If the trials were in Japan, what is the probability that all the defendants would be found guilty?”

Since P(0;10) is the likelihood that none of the defendants is found guilty, we want the complement 1-P(0;10)

but  

that for practical effects, can be considered equals 0, so the probability that all the defendants will be found guilty in 10 cases in Japan is practically 1.

The probability that all the defendants would be found guilty is 60% (P=0.5987).

Step-by-step explanation:

We can model this as a binomial distribution problem.

In Japan 95% of the defendants are found guilty, so there is a probability of 5% of being found innocent.

We can calculate the probability of having none of them found innocent as:

14.50

Step-by-step explanation: