I'm creating an activity for my class that teaches the vertical and horizontal line tests and for the life of me I can't figure out the probabilities involved. Here's the exercise:
Draw 5 pairs of cards from a standard deck. Each pair defines a point in the plane: the first card is the x-coordinate of a point and the second card is the y-coordinate (Jacks = 11, Queens = 12, Kings = 13). Red cards are positive and black cards are negative. Plot the 5 points, shuffle the cards, repeat the process to get a total of 10 points.
Question: What are the odds your graph passes the vertical line test?
This isn't the question the students will be answering, they are just calculating the experimental probabilities by polling the class. I thought it would be cool to show them the theoretical odds so we could discuss how close we are, but so far I've only been able to find simple, easy-to-understand wrong answers. I imagine it's pretty likely I've just forgotten some combinatorics and this is actually pretty easy to figure out.
(Update: About 34% is the most sensible answer I've gotten so far.)