A robbery has been committed and McGruff the crime fighting dog has been called in to investigate. He discovers that Sally Coldhands was seen wearing gloves in the neighbourhood shortly after the crime, and thus he concludes that she should be arrested. From the past experience, you know that 50 percent of the people Mcgruff says should be arrested for robbery are actually guilty. Before making the arrest, you order some additional investigation. From a large population of convicted robbers, you find that 60% wore gloves at the time of the crime and continued to wear them for an interval after the crime. Further investigations reveals that 80% of the people in the neighbourhood of the crime were wearing gloves around the time of the crime.
Based of the fact Sally was wearing gloves, what is the probability that Sally actually committed the crime? Hint: Answer is 0.43
This is a long question. I cant seem to derive 0.43 as the answer. I did probability trees but answer is different. Which led me to thinking if this is some kind of conditional probability question? Even so I cant seem to derive 0.43 as the answer.