• To frame the lesson, it can be helpful to discuss the factors that add pressure to “stand out” online. In the physical world, singles have their own filters in mind for the person who could become their significant other. However, there’s always a chance of meeting someone who is not “your type” on paper but who inspires a surprising connection nonetheless. In the virtual world, the filters are more absolute. If your profile doesn’t meet someone’s filter, there’s no chance of matching with them virtually. So, there’s also no chance of meeting up and forming a surprising connection. Therefore, the pressure to lie and get past the first virtual filter may be heightened in the online world.
• San Francisco residents tend to have higher incomes. Students may wonder if this could explain why the sample of OkCupid profiles tends to be so high-earning. Students may need to be reminded that the benchmark used to define a profile as “high-earning” in this data set is earning more than the median income among individual men living in San Francisco. So, geography alone can’t explain the high share of high-earning individuals.
• Many students find probability problems challenging. This is not because the probability formulas are too complex to learn. Rather, it’s often because probability word problems contain a lot of information. When reading through that information, it can be difficult to choose which formula best applies to the scenario (and what to “plug in” once a formula is chosen). Students often wonder, “Where do I even start?” So, this lesson introduces a framework we’ll use throughout the unit: rather than going straight to formulas, utilize the Keys to Probability. The first Key – Draw it first – is especially useful for solving probability problems. A visual representation, in the form of a Venn diagram, tree diagram (next lesson), or two-way table (following lesson), helps students deconstruct complex word problems and lay the information out in a familiar way. When students are wondering where to start, asking them to “draw it first” gives them a useful path forward.

First, download this lesson's slide deck and handout key to see the prompt and sample responses for the Lesson Starter. Then, check out the additional background notes below.

Instructional routine: Ten-Minute Talk. The lesson provides space for students to jot down their thoughts on the prompt, before discussing with a partner and engaging in whole group discussion. You can find more background on implementing a Ten-Minute talk here.

Purpose & Background: This Ten Minute Talk allows students to make sense of a Venn diagram by creating their own context and working backwards. While some students may have worked with such diagrams before, others may have never seen them in a formal setting. The prompt provides the opportunity to assess student experience with Venn diagrams as well as to clarify their understanding for precise use in statistics class.

First, download this lesson's handout key and read through its Discussion Question section. Then, check out our model discussion norms and the additional background notes below.

• Here’s a nice summary note you can share to wrap up the discussion: “Ultimately, when finding love, personal appearance matters far less than personal character. So, shoutout to all the honest Short Kings out there.”

• The full OkCupid data set can be found here. The data set in this lesson has a relatively small sample size (n = 192) due to several factors: dating apps hadn’t fully “taken off” by 2012, the geography of the data set is limited to San Francisco, the age is limited to 36 year olds (a less common age on dating apps, compared to younger age groups), and the data set is only composed of individuals that chose to make their profiles publicly viewable.
• Because the profiles listed in the data set are from individuals who chose to make their profiles publicly viewable, one could argue that this sample of individuals could be truly taller and higher income than the general public – hence, they have the confidence to set their profiles to be fully public. However, one could also make the case the other way: people making their profiles public have more of an incentive to lie, given the extra visibility on their profiles.

• Conditional probability is a powerful concept that connects to ideas throughout the course. Highlighting these connections in class can be helpful. For example, in Lesson 2.3, we explore how measures of job placement rates change given or conditional on the fact that students graduated. In Lesson 3.1, we calculate conditional distributions, which are the observed proportions given or conditional on a certain trait. The prominence of conditional probability throughout the study of statistics is why Harvard statistician Joseph Blitzstein calls conditioning the “soul of statistics.”
• When combined with the Multiplication Rule, the formula for conditional probability can be re-expressed as Bayes’ Theorem: \( P(A|B) = \frac{P(B|A)P(A)}{P(B)} \). Bayes’ Theorem is another powerful probability concept that’s slightly outside the scope of AP Statistics. As an extension activity, students can explore this New York Times lesson from a Skew The Script author, which utilizes conditional probability to introduce students to Bayes’ Theorem, along with the theorem’s sometimes unintuitive results.