In 2008 a college was shut down because of high rates of norovirus in the student population. The following table gives the numbers of male and female students who did and did not contract the virus at that time. We will let F and M represent the event that a randomly chosen student is female and male, respectively, and Y and N represent the event that a randomly chosen student contracted the norovirus or not, respectively. 

a. What is the value of P(Y) and what does it mean in the context of this situation? 

b. What is the value of P(Y|F) and what does it mean in the context of this situation? 

c. Are the events Y and F independent? Explain. 

d. Did males and females contract the norovirus at the same rates? 

e. If males and females contracted the norovirus at the same rates, would that mean the events Y and F have to be independent? Explain.

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Contracted norovirus Total Yes No Female Male 212 124 1,049 479 1,261 603 Total 336 1,528 1,864