Probability calculus minus the tricky jargon in a Statistics lecture

At last, lecturer Peter Verkoeijen is back in the auditorium, after two weeks of quarantining at home due to a corona infection. You would think that after two online lectures, students would be eager to pack the lecture hall. But the opposite is true: just one student is sitting in the auditorium.

The lecturer stands on the podium, behind him is a large screen with a PowerPoint presentation. He sports a wireless microphone with a receiver safely tucked away in his pocket. The whole setting conveys the feel of a TED Talk. Unfortunately, most of the audience is sitting at home. The lecture is broadcast live and will remain available on Panopto. Over fifty students are watching it live online.

Alya (Pedagogical Sciences) is the only one in the auditorium; she understands the choice of her fellow students. She usually follows the lectures from home as well. “Then I have more freedom in my planning and schedule,” she says. “But I still find today’s subject matter quite difficult, and here I can work in a more concentrated way and ask my questions directly.”

“Today, we’re going to discuss probability calculus,” says Verkoeijen as the lecture begins. “This part is difficult, but it is crucial to your research later on.”

In probability calculus, we are dealing with random phenomenons, the teacher explains. That is to say, we cannot predict the outcome. Nevertheless, the outcome does follow a regular order for a large number of repetitions. “So, it’s about how often something occurs in the event of a whole lot of repetitions,” he explains further. “Suppose we flip a coin to find out how often a certain side lands on top. If we toss it three or four times, there’s a good chance that one side will appear more often. But with a large number of repetitions, the probability of both sides turning up is about the same.”

The PowerPoint presentation features two Venn diagrams as a first exercise. Students have to solve probability puzzles. “So, I ‘ve got to use the general multiplication rule for this, right?” Alya asks. “Exactly”, the lecturer replies. “You can use that, but you can also solve it by using the Venn diagrams.” Alya then calculates the probability in her notebook and comes up with the correct answer. The teacher nods in satisfaction and then describes how students can figure out the answer without the formula.

During the calculation, you have to look carefully if it concerns a conditional probability. That means that the probability of A happening depends on event B. “What is the probability of you being dead if a shark bites your head off?” the lecturer asks. “That, of course, is one hundred percent. This is a conditional probability. A (death) happens if B (your head is bitten off by a shark) has taken place. But the other way round: how great is the chance that a shark bites your head off if you are dead? The chance of that is almost zero, because A (death) usually has nothing to do with B (a shark bite). There is therefore no conditional probability in this instance.”

As a final example, the teacher takes a page from the Dutch newspaper NRC Handelsblad. There are two sets of dots representing the number of vaccinated and unvaccinated people in the Netherlands. In the middle is a thickly framed circle representing the number of people who have tested positive for corona. The number of vaccinated and unvaccinated people in the circle is about the same.

“Here, you can see how important it is to look at the right kind of conditional probability,” the lecturer clarifies. “If you only look at people who have tested positive, then you could say that vaccinations don’t matter that much, because fifty per cent of the people who tested positive have also been vaccinated. But basically, you have to look inside the groups. In other words, how many people tested positive (event A) within the group of vaccinated people (event B). Then you can see here that the chance of testing positive is lower within the group of vaccinated people than within the unvaccinated people.”

At first, Alya was not keen on the subject at all she says during the break. “I have no background in Statistics, so for me it was really a case of catching up. But now that I understand the subject matter, I am starting to like it.” And that’s partly down to the lecturer’s explanations. “His explanations are easy to follow. He never uses difficult words without good reason. He also takes the time to go over difficult subject matter again very clearly. He never rushes through it as if everyone already has some prior understanding of it.”

Will she be attending the lecture again next time, or would she rather stay at home? I don’t know yet,” she smiles. “I really hope that more of my fellow students will show up to the next lecture. Because whenever I see on the registration page that the turnout is high, it also motivates me to come to the campus.”