You are interviewing patients who have been diagnosed with Diabetes as a follow-up for a recent treatment they have received. All the patients in question have been gathered in a waiting area while awaiting to be called in for the interview.
The patients have been classified by gender, as well as by the type of diabetes they have been diagnosed with (I or II). A summary of the number of patients falling into each category is as follows:
Summary of Diabetic Patients
Type I Type II
Male 36 12
Female 41 25
In order to speed up the process and minimize the time that your patients have to wait, you decide to call them in 3 at a time. You decide to get started and call in the first 3 patients, what is the probability that all three are females?
Express your answer as a percentage, rounded to 2 decimal places (e.g., for 0.42835, write 42.84, for 0.351 write 35.10).