A court of 3 judges declares an individual guilty when at least 2 of the 3 judges consider that this decision is justified. It will be admitted that if the accused is indeed guilty, each judge will rule in this direction with a probability of 0.7, independently of the 2 others. This probability drops to 0.2 if the accused is innocent. 70% of the accused are guilty. Calculate the probability that Judge 3 will vote guilty in each of the following situations:

(a) Judges 1 and 2 voted guilty; (b) Judge 1 voted guilty and judge 2 voted guilty

(c) Both judges 1 and 2 voted non-guilty