1. In a criminal trial, there are 25 persons who have been approved by both parties for possible inclusion in the eventual jury of 12. Of those who have been approved, there are 14 women and 11 men. If the judge forms the final jury of 12 by randomly selecting individ- uals from the approved listing, what is the probability that at least half of the eventual jurors will be males?
2. A computer firm must send a group of three specialists to give a technical presentation to a potential customer. Five such individuals are anxious to attend, but only two are considered to have strong interpersonal skills. Since the specialists have equal levels of seniority, they have agreed to place their names in a hat and allow management to randomly select the three to attend the presentation. What is the probability that there will be at least one person with strong interpersonal skills among the group that is sent?