On interview day, my two colleagues and I asked prospective students the courses they have taken until we found someone who hadn't taken a machine learning course. We had to ask 23, 18, 46 people respectively before finding someone who hadn't taken a machine learning course. What is the maximum likelihood estimate for the percentage of students that have taken a machine learning course? Remark. You can model this problem with a geometric distribution. Let p be the percentage of students that have taken a machine learning course. Then the probability of meeting N students is pN1(1p)