Question: Stat 238 versus Stat 241, Are both sufficient for Stat 242 and Stat 251?
Answer: Stat 238 and 241 overlap substantially but are quite different, and choosing one over the other involves tradeoffs. Overall I think they are both good courses and, from what I understand of your situation, you should feel free to choose either.
If you are planning to take further statistics courses such as 242 and 251, then the more standard choice would be 241, and I’d say you can’t go wrong with this choice. Stat 241 has been taught for a very long time, and the courses 242 and 251 were designed to follow 241.
Stat 238 was added to our course offerings much more recently. Our original question motivating the development of 238 was: for a student who is thinking of taking just one course in the whole area of probability/statistics/data analysis, hoping to learn as much as possible in one semester, what would we teach them? It has turned out that many Stat 238 students go on to take more statistics (including declaring a statistics major), but that was the original concept.
In contemplating taking Stat 241, you should definitely not worry about not having taken a statistics course before, and it is not true that 241 is less suitable for people with no prior experience with statistics than 238 is, since they both assume no prior experience with statistics, and just assume the mathematical prerequisite that you have.
What are those tradeoffs? Stat 241 focuses on probability theory and tends to emphasize mathematical developments more, and Stat 238 includes a substantial amount of statistics and computing together with some math. That is, typically (of course it varies with different instructors) Stat 241 feels more like a math class, and Stat 238 mixes in statistical inference (from a Bayesian viewpoint, which is a bit unusual for a course at this level), computing, and some data analysis. You can expect to get more time and practice and depth with Probability Theory in 241 than in 238. Stat 238 includes topics that overlap (but from a somewhat different point of view and perhaps for different purposes) with 242 and 251, such as using likelihood for statistical inference (which also is done in 242) and Markov chains (which are also done in 251). From that point of view, students who come out of Stat 238 and then take 242 or 252 may feel that they are already comfortable with some concepts that others in those classes are seeing for the first time, which could be viewed as an advantage, but they may feel that their command of probability theory is being taxed more than the students coming out of 241, which is a disadvantage.
In 238 I would say you get enough probability theory that you are prepared to take 242 and 251, and in this regard differences between how well individual students “got” the respective classes (238 or 241) are probably more important than which class they took, but the median student in 241 probably has a more solid command of probability theory than the median student in 238. The 238 students probably have some additional useful perspectives and insights (as well as skills in computing and simulation) that could help them understand and appreciate some of the things they are about to learn in 242 and 251, and the hope would be if they feel a need to strengthen any particular aspect of probability theory while taking 242 and 251, it would not be a problem to do some review or a bit of extra reading, perhaps in a Stat 241 textbook.