If you're teaching probability and you're looking for a humorous way to discuss independent events, I may have one for you. On an episode of The Daily Show on CBS, host Stephen Colbert explained his strategy of winning an upcoming lottery. His logic doesn't quite work out as you'll see in this 74-second clip from the show. Can your students figure out why?
Statistics professor and community member @Scott_Crawford explained this faulty reasoning in response to another post in the community in which he said,
This is similar to the joke about the statistician who was caught bringing a bomb onto the plane. When interrogated he said "Well, I knew that the probability of someone bringing a bomb on the plane was 0.0006 but I decided that was still too high, so I looked at the probability of two people bringing a bomb, and that was 0.00000036 and that was much safer so I brought a bomb, and that way I can feel certain no one else has one".
The issue is independence. P(A and B) = P(A)*P(B) but if you know B has already happened it doesn't change the probability of A. So P(A given B) = P(A)
In other words, because of independence, you bringing a bomb on the plane doesn't alter the probability of someone else having a bomb on the plane. Likewise buying a lottery ticket doesn't alter the probability of someone buying the same ticket.
If you'd like to use this video for one of your questions in WebAssign, feel free to duplicate this question:
Your Chances of Winning the Lottery (4244138)
You'll also find these WebAssign assignments which cover the topic of independent events:
Independent Events and Bayes' Thm: 1027240,1221402, and 7434538