I believe that all of these are binomial distribution problems, but I'm not really sure how to approach them. Any help would be appreciated greatly.
1. Estimate the probability that, in a group of five people, at least two of them have the same zodiacal sign. (There are 12 zodiacal signs; assume that each sign is equally likely for any person.)
2. 30% of the workers in a workforce are women. A company hires 100 workers of which 25 are women. What is the probability this (the hiring of 24 women or less) occurred by chance?
3. To ensure a high male/female ratio, the ruler of a mythical island decrees couples may keep having children until they have a girl. If the decree is followed, what will the male/female ratio be on the island?