Odds of getting accepted to a medical school. A simple mathematical model.
A simple Binomial probability distribution based mathematical model can highlight the impact of number of schools a student applies to his/her/their odds of obtaining an acceptance.
A common question we get is “What is the probability of getting accepted into a medical school?” Getting into a medical school depends on several factors – GPA, test scores, essays, letters of recommendations, yield management decision of colleges, your luck, and more.
A related question is “What can we do to increase out odds of getting accepted?” i.e. things that we can control and possibly influence. One factor under the control of students is the number of colleges to apply and the list of colleges to apply.
A mathematical model can offer some guidance into number of schools to apply. One way to look at the mathematics of acceptance is to rely on Binomial probabilities. We present a simplified model which one looks at the number of applications and its impact on potential medical school acceptance.
Let us denote p as the
acceptance rate at a university i.e. success.
For my example, I have assumed this to be constant and equal to 2.4% (that is
approximately the average acceptance rate based on AAMC application data).
Thus, p = 0.024
Let us denote q as the failure rate.
Now, we know
q = 1 - p
q = 1 - 0.024
q = 0.976
Probability of getting AT LEAST 1 acceptance = 1 - probability of getting ZERO acceptances
Binomial probability is given by this formula: nCr * p^n * q^(1-n)
Where
n = number of program one applies to
r = number of acceptances
nCr = Binomial coefficient in combination format
Let’s assume you apply
to 15 programs, n = 15
Probability of getting ZERO acceptance means r = 0
Probability of getting ZERO acceptance = P(r = 0)
P(r=0) = 15 C 0 * (0.024)^0 * (0.976)^15
P(r=0) = 0.69461997
Probability of getting AT LEAST 1 acceptance = P(r >=1) = 1 - P(r=0)
P(r>=1) = 1 -
0.69461997
P(r>=1) = 0.30538003 OR 30.54%
If you apply to 15 colleges, there is 30.54% chance you will get at least 1 acceptance.
Here is the probability of getting AT LEAST 1 acceptance for various N (number of applications): Please refer to chart below.
NOTE:
- You need to apply to 29 colleges for your probability to be greater than 50%.
- You need to apply to 21 colleges for your probability to be nearly 40%
One can use different probabilities and play around with this model. But the key to remember is that this is just based on mathematical model - in actual practice, a lot of factors are in play!
While this is a simple exercise, we should ideally do conditional probability – probability of getting accepted conditional on getting an interview. Also this simple model does not factor any impact of GPA, test scores, and other factors. It is just to highlight how the number of applications may impact your odds.
The number of schools to apply will remain a decision that parents and students have to take. Models can show some insights but the decision on how many schools to apply needs to factor in individual circumstances, effort, cost, and time availability.
PS: The contents of this article were shared in one of the public forums last year as part of forum discussions.
