# Engaging students: Independent and dependent events

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Danielle Pope. Her topic, from Probability: independent and dependent events.

What interesting (i.e., uncontrived) word problems using this topic can your students do now?

Students use the idea of independent and dependent events in their lives without even realizing it. Many of the word problems used to introduce probability are basic concepts that students can understand. The basic definition of an independent event is “the probability that one event occurs in no way affects the probability of the other event occurring”. Word problems can be used to demonstrate this. Asking if the probability of flipping a coin changes if you were to roll a die as well is a prime example. These two acts are something that can be easily implemented in the classroom and the technical definition can be taught. Students can then help come up with more scenarios and teach themselves the terms. Similarly this idea can be used for dependent variables with a few changes. If the “probability of one event occurring influences the likelihood of the other event” then the event is defined as dependent. Word problems could be “if you were to draw two cards from a deck of 52 cards and if on your first draw you had an ace and you put that aside, would the probability of drawing another ace change? This card questions could be more challenging by taking out more cards each time.

How can this topic be used in your students’ future courses in mathematics or science?

The topic of independent and dependent events can later be translated into variables when used with functions in Algebra class. Knowing and understanding the difference will help students know how to classify an event and use the correct variable and axis if asked to sketch a list of data. Just in a probability course students will learn about conditional probability, which will use the idea of dependence. Other terminology like with replacement and without replacement will be used to define a dependent event in probability. This topic can even be translated into a physics classroom when talking about time, position, velocity, acceleration etc. For example, when calculating the velocity students will either find or be given the displacement and change in time. Not knowing that the dependent event divides the independent variable or specifically with velocity, displacement divides time, If those numbers are not plugged in correctly then that will lead to the wrong answer.

How has this topic appeared in the news?

In the news, independent and dependent events show up everyday. The most common example is weather. One of the longest debates that we have been having is if global warming and climate change has influenced the world. According to an article in the Smithsonian Magazine, scientists “couldn’t prove that global warming had “caused” the heat wave of 2003, (they) did assert that warming from human emissions had doubled the risk of extreme weather events.” This observation can then be taken to a student’s science class and they can research the risk of continuing this pattern of damage to Earth. Natural disasters can also have a say in many events around the world. For example just recently “Gas prices spiked in the Baltimore-area — and nationwide — in recent days and are expected to continue to rise after a major pipeline that runs from Texas to the East Coast had to be shut down following Hurricane Harvey”. This is a prime example of a dependent event. This shortage in gas specifically in Texas then led to many people rushing to fill up their cars, resulting in gas stations running out of gas, which is just another example of dependent events.

References:

Rules of Probability and Independent Events

http://www.smithsonianmag.com/science-nature/does-climate-change-cause-extreme-weather-events-180964506/