There are 297 students. 71 students are seniors, and out of the 71 students, 53 participate in a sport (while 18 do not participate in a sport). Among those who are not seniors, 69 students participate in a sport and 157 do not. Suppose we choose one student at random from the entire class.
A. Are events "drawing someone who is a senior" and "drawing someone who does not play a sport" mutually exclusive? Why/why not?
B. Are events "drawing someone who is a senior" and "drawing someone who does not play a sport" independent? Why/why not?
(C-E) Suppose you draw five students at random without replacement.
C. What is the conditional probability that the second student drawn is a senior, if the first student drawn is a senior?
D. What is the probability that the second student drawn is a senior, without knowing anything about the first student?
E. What is the probability that among the five students, none of them are seniors?
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