The following contingency table summarizes the school enrollment by level and type:

	Public ($\displaystyle {T}{1}$ )	Private ($\displaystyle {T}{2}$ )	Total
Elementary School ($\displaystyle {L}{1}$ )	379	77
Middle School ($\displaystyle {L}{2}$ )	176	53
High School ($\displaystyle {L}{3}$ )	199	97
Total

1. For a randomly selected student, describe the following in words:
   • $\displaystyle {T}{2}$  is Select an answer an event in which a randomly selected student is in Public an event in which a randomly selected student is in High School an event in which a randomly selected student is in Private an event in which a randomly selected student is in Elementary School an event in which a randomly selected student is in Middle School
   • $\displaystyle {P}{\left({T}{2}\right)}$  is Select an answer the probability that a randomly selected student is in High School the probability that a randomly selected student is in Private the probability that a randomly selected student is in Middle School the probability that a randomly selected student is in Public the probability that a randomly selected student is in Elementary School
2. Find the following probabilities: (Round the answers to 4 decimal places)
   
   1.  $\displaystyle {P}{\left({L}{3}\right)}=$
   2.  $\displaystyle {P}{\left({T}{2}\right)}=$
   3.  $\displaystyle {P}{\left({L}{2}\cap{T}{2}\right)}=$
   4.  $\displaystyle {P}{\left({L}{1}\cup{T}{2}\right)}=$
   5.  $\displaystyle {P}{\left({L}{3}{\mid}{T}{1}\right)}=$
3. Answer the following questions:
   1. Are $\displaystyle {L}{1}$ and $\displaystyle {T}{1}$ mutually exclusive? Select an answer not mutually exclusive mutually exclusive Explain. Select an answer Because the probability of one event doesn't depend on whether the other occured or not Because the probability of one event depends on whether the other occured or not Because the two events can not occur at the same time Because the two events can occur at the same time
   2. Are $\displaystyle {L}{1}$ and $\displaystyle {T}{1}$ independent? Select an answer independent dependent Explain. Select an answer Because the two events can occur at the same time Because the probability of one event doesn't depend on whether the other occured or not Because the probability of one event depends on whether the other occured or not Because the two events can not occur at the same time
   3. Are $\displaystyle {L}{3}$  and $\displaystyle {L}{2}$  mutually exclusive? Select an answer mutually exclusive not mutually exclusive Explain. Select an answer Because the two events can not occur at the same time Because the probability of one event doesn't depend on whether the other occured or not Because the two events can occur at the same time Because the probability of one event depends on whether the other occured or not
   4. Are $\displaystyle {L}{3}$  and $\displaystyle {L}{2}$  independent? Select an answer independent dependent Explain. Select an answer Because the two events can not occur at the same time Because the probability of one event doesn't depend on whether the other occured or not Because the two events can occur at the same time Because the probability of one event depends on whether the other occured or not