# Does this probability example I made look correct?

There are 129 med schools in the US.

There are 28 vet schools in the US.

if 10,000 students apply to vet school and 10,000 students apply to med school, and every school can only accept 50 applicants, what would be the probability an applicant would get accepted in either type of school?

This means that if you apply to vet school under these circumstances, you will have a 14% chance of being accepted into vet school. If you apply to med school under these circumstances, you will have a 64.5% chance of being accepted into med school

• Well, you should specify that you are making the extremely unrealistic assumption that each applicant is equally likely to get into each school.
– lulu
Dec 9 '16 at 22:39
• oh I understand that. this is for a paper and each paragraph of my paper states an obstacle that makes getting into vet school difficult. This paragraph (not shown in question) stated that this example is strictly based off of how hard it is to get into vet school based on the limited numbers there are in the US. As i go along I will add onto this problem by adding other scenarios such as gpa, experience etc. Dec 9 '16 at 22:49
• Well, if it's really true that the number of applicants to vet school is roughly the same as the number of applicants to med schools, but there are $4.6$ times as many med schools (and that the schools take the same numbers) then I'd tend to agree that this represented an obstacle. Fair enough.
– lulu
Dec 9 '16 at 22:54
• I am making all variables other than the number of schools the same to make my statement true. These are not factual numbers Dec 9 '16 at 22:58
• Well, if you are trying to describe a real issue in the real world, I'd try to approximate real numbers. I just used google to get $48014$ for medical school applicants and $6744$ for vet schools...not sure the numbers are supporting your claim here. But, enough. I would advise stressing that the numbers you are using are not realistic, but that is up to you.
– lulu
Dec 9 '16 at 23:04

This is true under the condition that every applicant has an equal probability of being accepted. That obviously is not true in the real world, but it could make a homework exercise that is helpful for educational purposes. If that is what you are intending, you need to make sure you clarify that every applicant has an equal probability of being accepted.

• okay good suggestion. I'm using it to suggest in a paper that vet school is harder to get into vs med school because of the limited number of vet schools. All other things were made equal to make my statement true. Should I put at the end of the question "based solely on the information given"? Dec 9 '16 at 22:43
• Yes, it would be good to clarify that it is only true under the assumptions that you make. However, if you are writing this in a paper that will be read by educated people, In my opinion you should rethink the statement that vet school is harder to get in to. You would need a more information to make such a claim with legitimacy. For example, what do the grades and test scores look like for people applying to vet school vs. people applying to medical school? Dec 9 '16 at 22:53
• Each paragraph states a reason why vet school is difficult to get into and since this paper is for my statistics class I am including a statistics problem for each paragraph to prove my statement correct. After this paragraph, I will move on to the grades and grade point average and how it affects applicants in getting into vet schools. I may or may not use some of the same information in the problem I did above for my next paragraph. I will probably build onto it Dec 9 '16 at 23:02
• Sounds good. I just realised I didn't answer you question in your comment very well. Yes, it would be good to have "based solely on the information given" at the end of the question (and again, be sure to clarify the assumption that everyone has equal probability of being accepted). Dec 9 '16 at 23:05
• okay thanks for the feedback! Dec 9 '16 at 23:10

Note, I think the independence of these events is important here. It better be stated whether they are independent or not. The way that you found the probabilities in the beginning seems right. However consider the following: This is the same probability as the compliment of being accepted to both. P(Accepted to both)= 1 - P(Accepted to strictly either OR NONE). P(Accepted to strictly either OR NONE) = ... Does this hint help ?