A robbery has been committed and McGuff, the crime-fighting dog, has been called in to investigate. He discovers that Sally Coldhands was seen wearing gloves in the neighborhood shortly after the crime, and, thus, he concludes that she should be arrested. From past experience you know that 50% of the people that McGuff 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 investigation reveals that 80% of the people in the neighborhood of the crime were wearing gloves around the time of the crime.
a. Based on the fact that Sally was wearing gloves, what is the probability that Sally actually committed the crime?
b. If you charged her with the crime, do you think a jury would convict her based on the glove evidence? Explain why or why not.