Week 5 Discussion — Is It Really Due? — Traditional alternative (no AI)

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

Hook

A team on a losing streak is "due" for a win. A bus that was late three days running is "bound" to be on time. Knowing which island a penguin lives on changes your best guess about its species. This week you learned the rules that say when a chance changes and when it does not, which means you can now test claims like these instead of taking them on faith.

Your discussion question — choose Option A or Option B; they carry the same weight and the same rubric, and you say which you picked.

Option A: Think of a real time you or someone you know said an outcome was "due" or "on a streak": a sports team, a game, a run of rainy days, a series of late buses, anything. Decide whether the trials in your example are independent, use the law of large numbers to explain what the long run does and does not promise, and say whether the "due" reasoning holds up.

Option B: Pick a situation from your major, your job, or your community where knowing one fact might change the chance of another, such as whether a reminder text changes the chance a patient keeps an appointment. Say which conditional probability you would compare with which overall probability, explain why swapping the condition would mislead, and say whether finding a dependence would show that one thing causes the other.

There is no single right answer. A losing streak in a game of skill, a run of late buses on a road under construction, or a reminder text that only some patients receive can each be argued well in more than one direction. Pick one you actually care about, and tell us the story.

Expectations

Activity format: one initial post followed by two substantive peer replies. Plan on about 45 minutes across the two deadlines; your instructor sets both due dates in Canvas.

Your initial post — by the first due date (early in the module week):

• Say which option you chose.
• Describe your real example in plain words, so a reader who was not there knows what happened.
• Use at least two of this week's terms (probability, law of large numbers, gambler's fallacy, sample space, event, complement, mutually exclusive, independent events, dependent events, conditional probability) correctly.
• Give your judgment, independent or not, due or not, or which conditional probability you would compare, with a reason.
• Length: roughly 150–250 words if written. You may instead record your post as audio or video (about two minutes) and attach a transcript; both forms are scored by the same rubric.

Your replies — by the second due date (the end of the module week):

• Reply substantively to at least two classmates.
• A substantive reply does more than agree: question whether the poster's events are really independent, point out a condition read the wrong way around, or suggest a lurking variable behind a dependence. "Nice point!" on its own does not count.

What a strong post looks like:

I chose Option A. My cousin says her favorite slot game is due to pay out because it has not paid in an hour. Each spin is a separate trial, and nothing about the last hour changes the machine's chance on the next spin, so the spins are independent events. The law of large numbers says the share of winning spins settles over a very long run; it does not promise a win soon to make up for the dry spell. That is the gambler's fallacy.

Notice how it names the trials, checks independence with a reason, and uses this week's terms precisely. That is the bar.

Participation rubric

This discussion is worth 10 points. The three criteria below look at your initial post and your peer replies.

Post early if you can — the best threads happen when people have time to reply before the second due date.

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