(6) 8 friends are doing a secret Santa gift exchange. Each friend picks a name out of a hat and keeps it (unless they draw their own name, in which case they put the name back and redraw). What is the probability that at least two people pick each other? (7) Rabbits and mice are being tested in a maze, with the goal of finishing for a prize. Suppose 30% of the rabbits in the experiment received finished the maze, whereas 25% of the mice finished. 60% of the animals being tested are rabbits. Given that an animal chosen at random finished the maze, what is the probability that it was a rabbit?(8) Company A supplies 40% of the computers sold and is late 5% of the time. Company B supplies 30% of the computers sold and is late 3% of the time. Company C supplies another 30% and is late 2.5% of the time. A computer arrives late - what is the probability that it came from Company A? (9) In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty. (a) If one of the study subjects is randomly selected, nd the probability of getting someone who was not sent to prison. (b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, nd the probability that this person was not sent to prison