Answer:
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
[tex]\large P(k;n)=\binom{n}{k}p^kq^{n-k}[/tex]
where
[tex]\large \binom{n}{k}[/tex]= 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
[tex]\large P(0;10)=0.05^{10}=9.7656*10^{-14}[/tex]
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.
Answer:
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:
[tex]P(I=k)=\frac{n!}{k!(n-k)!}*p^k*(1-p)^{n-k} \\\\P(I=0)=\frac{10!}{0!10!}*0.05^0*0.95^{10}\\\\P(I=0)=1*1*0.5987\\\\P(I=0)=0.5987[/tex]
