Hi,I need a help with my homework. It's about probability.
A random murder mystery Miss Mac’s sharp powers of interrogation and deduction quickly produced two suspects. · Adeline Apple, Sir Harry’s middle-aged daughter and sole heir to the Apple estate. Adeline also worked as a circus performer (with a knife throwing act), her father having insisted that she work to support herself and denied her any financial support so that she not become lazy and dependent on the family fortune. · The Butler, a servant of the household for many decades and cleanliness fanatic. Despite long and loyal service, he had always been treated arrogantly and thoughtlessly by Sir Harry. Miss Mac was convinced that there were no suspects other than these two. She proceeded to her room to individually question some of those who claimed to have information. QUESTIONS 1. Miss Mac wondered if Adeline might be guilty of murdering her father. She certainly had a financial motive to do so! George the Gardener stomped into Miss Mac’s room and claimed that he had seen Adeline was outside in the garden adjacent to the main house at around the time the murder occurred, and that Agatha therefore could not be the murderer. Miss Mac, ever alert, observed his nervousness and unwillingness to look her in the eye, and felt uncertain about this story. George left, and she pondered on his truthfulness, or otherwise. If Adeline truly were in the garden then it might seem she couldn’t be the murderer... except that, as an accomplished knife thrower, she could have struck Sir Harry with a well-aimed throw straight through the open dining room window! Such a throw seemed possible but unlikely, Miss Mac mused, and she assigned a probability of 0.1 to Adeline being the murderer if she had actually been outside. However if Adeline had been inside after all, and George had been lying, then Adeline seemed a much more likely suspect. Miss Mac assigned a probability of 0.8 of Adeline being the murderer had she actually been inside the house at the time. After some more deep thought, and refreshed by nice cup of tea, Miss Mac determined her probability that Adeline was the murderer to be 0.6. What probability did Miss Mac assign to the truth of George the Gardener’s story about Adeline being outside in the garden? 2. Miss Mac next turned her little grey cells to The Butler. Simply because he was a butler, Miss Mac thought it was a 50/50 chance that he was the murderer; it was just as likely that he was the murderer as that he wasn’t. But then Hedley the Housekeeper, who had delivered the tea, volunteered that as she rushed past the kitchen on the way to the adjacent dining room to investigate all the noise, she had seen The Butler vigorously washing his hands... (Hedley wondered aloud if he might have been washing blood off his hands?) Miss Mac asked for more tea as she thought about this new information. She trusted Hedley’s account of what she had seen, but The Butler was a known cleanliness fanatic while vigorous handwashing at that late hour might seem a little odd, she thought that if he had not been murdering Sir Harry next door there would still be a 25% chance that he would be washing his hands like that anyway. On the other hand, if he had just been murdering his boss, it was very likely, say 95%, that he would have been cleaning his hands as if his life depended on it (which it just might!). How does Miss Mac update her probability that The Butler is the murderer? 3. Following these investigations and probability calculations, does Miss Mac think that Adeline and The Butler are both guilty? (eg. they could have cooperated to make the murder happen.) What probability does she assign to this? 4. Are these relative frequency or subjective probabilities? Briefly explain.