A person tried by a 3 -judge panel is declared guilty if at...

A person tried by a 3 -judge panel is declared guilty if at least 2 judges cast votes of guilty. Suppose that when the defendant is in fact guilty, each judge will independently vote guilty with probability $.7,$ whereas when the defendant is in fact innocent, this probability drops to $.2 .$ If 70 percent of defendants are guilty, compute the conditional probability that judge number 3 votes guilty given that (a) judges 1 and 2 vote guilty; (b) judges 1 and 2 cast 1 guilty and 1 not guilty vote; (c) judges 1 and 2 both cast not guilty votes. Let $E_{i}, i=1,2,3$ denote the event that judge $i$ casts a guilty vote. Are these events independent? Are they conditionally independent? Explain.

Transcript

00:01 All right, so let make a trial here, right? so let this will be a trial and let this will be 0 .8 and this point this will be guilty right? this will be guilty and this will be 0 .2 and let bust this is let this is so let judge 1 will be guilty of 0 .7, right? and judge 2 will be also guilty of 0 .7.

00:48 And judge 3 will be also guilty of 0 .7, right? and this total will be 0 .27, right? now here this will be judge one will be guilty of 0 .7 and judge 2 will also guilty of 0 .7 and here judge 3 will also be guilty.

01:23 This will be non -guilty right? this will be not guilty.

01:29 This will be not guilty.

01:30 This will be not guilty of 0 .3.

01:33 Right and the total is 0 .12 right now here judge 1 will be guilty of 0 .7 vote and judge 2 will be not guilty of 0 .3 right and judge 3 will be guilty 0 .7 right and judge 3 will be guilty 0 .7 and this will be 0 .12 right now here here, this is the fourth branch, right? so this will be, judge 1 will be guilty of 0 .7.

02:22 And here, judge 2 will also be not guilty of 0 .3.

02:29 And judge 3 will be not guilty of 0 .3.

02:34 And all this will be 0 .05, right? so now let make an assumption that the probability of judge 1 will be guilty and the probability of guilty is 0 .7, right? and also the probability of judge 2 will be guilty and this is 0 .7.

03:01 And also the probability of judge 3 guilty, this will also be 0 .7, right? now the probability of judge 1 will not guilty, this will be 0 .3.

03:20 And the probability of when judge 2 is not voted guilty, this will be 0 .3.

03:29 And the probability of judge 3 will not guilty, this will be also 0 .3...

Question

Please give Ace some feedback