There are $12$ freshmen and $17$ sophomore students in a classroom. We randomly select two

students.

Suppose the students were selected with replacement.

a$)$ If the first student was a freshman, what is the probability that the $2$ nd student is also a

freshman?

b$)$ If the first student was a sophomore, what is the probability that the $2$ nd student was a

freshman?

Suppose the students were selected without replacement.

c$)$ If the first student was a freshman, what is the probability that the $2nd$ student is also a

freshman?

d$)$ If the first student was a sophomore, what is the probability that the $2$ nd student was a

freshman?

Be sure to include at least $4$ decimal places, if needed.

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