The areas of statistics and probability are my favorite in mathematics. This is because I like to be able to draw conclusions from data and predict the future with past trends. Probability is also fascinating to me since it allows us to make more educated decisions about real-life events. Since we are supposed to get a big snow storm in Waterloo, I thought I would write a blog post discussing conditional probability using the Probability Tree Generator, created by Miles Simmons.

If the probability of snowfall on any given day during a Waterloo winter is 0.75, the probability that the schools are closed given that it has snowed is 0.6, and the probability that the schools are closed given that it has hasn’t snowed is 0.1, then we get the following probability tree, created by Miles’s learn document:

From this information we can come to some interesting conclusions:

What is the probability that the schools are closed on a given day?

From the Law of total probability, we get:

Thus, during a very snowy Waterloo winter, we could expect a 0.475 chance of schools being closed on any given day. 

One of the features of this document is that the node probabilities are calculated. You can see this by comparing the second last step to the number at the end of probability trees' nodes.

What is the probability that it has snowed given that the schools are closed?

From Bayes’ Theorem, we get:

Thus, during a very snowy Waterloo winter, we expect there to be a probability of 0.947 that it has snowed if the schools are closed. 

We can also add more events to the tree. For example, if the students are happy or sad given that the schools are open:

Even though we would all love schools to be closed 47.5% of the winter days in Waterloo, these numbers were just for fun. So, the next time you are hoping for a snow day, make sure to wear your pajamas inside out and sleep with a spoon under your pillow that night!

To explore more probability tree fun, be sure to check out Miles’s Probability Tree Generator, where you can create your own probability trees with automatically calculated node probabilities and export your tree to a blank Maple Learn document. Finally, if you are interested in seeing more of our probability collection, you can find it here!

Have you ever wondered who the students are that help create Maplesoft’s family of products?

In this blog, we thought that it was fitting to introduce ourselves and give the MaplePrimes community some insight into the students who are committed to helping Maplesoft improve its products and who believe that Math Matters!

I’ll begin. My name is Jack Thomson and I’m in my second year of the Mathematics (Waterloo) and Business Administration (Laurier) Double Degree. This term I am the Product Management Co-op at Maplesoft where I will be helping support the development of Maplesoft's academic market products, including Maple Learn and Maple Calculator. My favorite areas of math are statistics and probability. These areas are my favorite since I like to be able to draw conclusions from data and predict the future with past trends. I am also fascinated with probability since it allows us to make more educated decisions about real-life events. This ties into my belief of why Math Matters, since it is hidden in every aspect of life and helps us understand the world around us. Besides my love for the world of mathematics, I love the outdoors, more specifically, mountain biking, backcountry camping, and skiing. I also enjoy taking photos, watching Formula 1, playing hockey, and improving my skills in the kitchen.

Continue reading below to find out more about my fellow Co-op students!

Development:

I’m Zhengmao (he/him), and I’m a third year in Software Engineering at the University of Waterloo. I’ll be working until the end of April here at Maplesoft as a Software Developer, where I’ll be working to fix bugs, add new features, and improve existing ones for our Maple Learn as well as Maple Calculator products. By the way, if you ever have any suggestions or ideas about them, don’t hesitate to reach out to me!

I’ve always been curious about working at a math company because I’ve always been so interested in math. In fact, Maplesoft is the only company I’ve consistently applied to every time I’ve gone through the Co-op application cycle! However, there’s not really any particular reason why I enjoy the subject. I find math to be beautiful in and of itself, almost like an art, and I find the kinds of math that are more discrete or algebraic tend to be a little nicer. As long as there aren’t decimals, I’m pretty happy. So, my ideal kind of math is just that: ideal! Exact values, unrealistic ideas, and as few numbers as possible. In terms of my university career, I’ve always enjoyed linear algebra much more than calculus.

Overall, I’m quite excited for this term at Maplesoft. I’ve never worked in web or mobile development before, so I’m looking forward to learning a lot of new things!

Content Creation:

Hi, I’m Paige (she/her). I am a second-year Honors Mathematics student at the University of Waterloo. This term, I am creating content for the Maple Learn document gallery. My favorite area of math is calculus because I love visualizing functions. Math matters because it is a universal language. All the math concepts we know are naturally occurring; people have observed and documented them, but no one invented them. Because of this, people from a wide range of cultures have come to the same conclusions (ex: defining pi). Math is universally understandable, which is why it can be used to connect everyone on earth (and maybe on other planets too!?!?!?!). In my free time, I like doing hand embroidery, playing video games, and cuddling my cat Licky.