What equations do I need to use to solve the following equations? I am struggling.

-If one-third of the University of Wisconsin teaching assistants (TAs) sign a petition calling for a collective bargaining election, an election will be held. A survey of 50 TAs indicates that 40% will sign the petition. What is the probability that a sample such as this could have occurred if one-third or fewer of the TAs in the population will sign such a petition?

-The mean number of persons shot by the Metro City Police Department in an hour is 0.042. What is the probability that the MPD will shoot no one in a 24-hour period? What is the probability that the MPD will shoot one person? Two persons? More than two persons? Explain your work.

-The mean number of major fires in Flandreau, South Dakota, is 0.057 on any given day. What is the probability that no major fires occurring in any given week? What is the probability of one major fire? Two major fires? Three or more major fires?

-The mean number of murders reported in Metro City during the 8-hour graveyard shift is 0.5 for any hour. It takes two people two hours to investigate a homicide call. How many officers should be assigned to the homicide squad during these hours?

-The Madison Fire Department's files reveal that an average of six firefighters a year suffer heart attacks while on duty. The personnel office is concerned about this because it must budget funds for disabilities. There are some concerns that the physical condition of firefighters is getting worse. This year, nine firefighters suffered heart attacks. What is the probability that an event of this severity will occur? Given past history, what is the probability that no heart attacks will occur? Exactly one? Exactly two? Three or fewer?