In science museums, you’ll often f nd what’s called a probability board (also known as a quincunx ): This is like a big, shallow, tilted baking pan with a slot at the midpoint of the top edge through which marbles roll, one at a time, from a reservoir outside the board; let’s say the reservoir has k marbles in it. Just below the slot is a f xed peg, which each incoming marble hits and causes the marble to roll left or right off of; assume that you’ve tilted the board so that there’s an equal chance that the marble will roll left vs. right (interpret “left” and “right” from your viewpoint as you look at the board from in front of it, which is the opposite from the marbles’ viewpoint as they dive down the board nose f rst on their stomachs). Below this peg is a row of two pegs, parallel to the top edge of the board but offset horizontally from the f rst peg so that the two pegs in this second row are diagonally arranged below the f rst peg, as in the picture. Assume that the board’s tilt angle, the peg spacing, the marbles’ mass, and the gravitational f eld of kel01315_ch03_053-120.indd 113 17/12/13 10:11 AM 114 Chapter 3 the host planet are just right so that each marble will next hit exactly one of the two pegs in the second row (which peg it hits is determined by whether it rolled left or right off of the f rst peg). The marble will next roll left or right off of whichever peg it hits in the second row (again, assume a