In biomedical research, dealing with probabilities is part of the daily routine for many scientists, independently of their specific research area. Statistics and probability calculations are important during the design phase of experiments (e.g., for group size calculation and power estimations), as well as during the analysis of study results and outcomes.
However, for researchers not familiarized with statistics, probability calculations can be puzzling, as we’ve got very strong instincts about how we expect numbers to work. The following example, called the Birthday Paradox, shows how misleading our instincts and intuition can be:
Let’s consider the probability that at least two individuals in a given group of n randomly selected people have the same birthday (under the assumptions that each day of the year is equally probable for a birthday, and that all the birthdays are independent). Imagine a classroom of 30 children. What’s the probability that two of the children have the same birthday? 365 possible birthdays, and only 30 children in a classroom? Intuition would say it’s pretty unlikely.