"suppose the fraction of undergraduate students who smoke is 15% and the fraction of graduate students who smoke is 23%. if one-fifth of the college students are graduate students and the rest are undergraduates, what is the probability that a student who smokes is a graduate student? given the information in part (a), is a randomly chosen college student more likely to be a graduate or undergraduate student?
b. repeat part (b) assuming that the student is a smoker."

What is the probability that a student who smokes is a graduate student?
What we want to find is: P(G|S)
P(A) = Probability of A
P(A∩B) = Probability of A and B
P(A|B) = Probability of A, given B
U = Undergrad'
G = Graduate
S = Smoker
We just have to use the formula:
P(G|S) = P(G∩S)/P(S)
The statistics given are independent of one another, i.e. they don't  affect one another, this means:
P(A∩B) = P(A) * P(B)
So:
P(G∩S) = 0.2 * 0.23 = 0.046
P(S) = (0.2 * 0.23) + (0.8 * 0.15)
= 0.046 + 0.12 = 0.166
Therefore:
P(G|S) = 0.046/0.166 = 0.2771 ⇒ 0.28 (28%)

A randomly chosen student is more likely to be an undergrad as they comprise 4/5 or 0.8 or 80% of the student body.
Assuming they are a smoker, a randomly chosen student is still more likely to be an undergrad.
We worked out for the first part the probability a student is a graduate and a smoker and found there is only a 28% chance of randomly selecting a graduate from among the smokers.
This means there is a 72% chance you will select an undergrad.

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.