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Fair Games

August 6, 2008

We continued our probability and statistics gig Tuesday by playing some simple games. In each case, the kids were asked, is this game fair? What do you predict will happen?

  • (very easy) Flip a coin. If it lands on heads I get a point; if it lands on tails, you get a point. (Fair, each person has a 1:2 — or 50% — chance of scoring)
  • (very easy) Spin a spinner equally divided among 4 colors: red, blue, yellow & green. If we spin red, I get a point; if we spin blue, you get a point. (Fair, each person has a 2:4 — or 1:2 — or 50% — chance of scoring)
  • (easy) Spin the same 4-color spinner. If we spin a “cool” color, I score a point; if we spin a “hot” color, you get a point. (Fair — there are 2 cool colors (blue & green) & 2 hot colors (red & orange): each person has a 1:2 — or 50% — chance of scoring)
  • (easy) Spin the same 4-color spinner. If we spin a primary color, I score a point; if we spin a non-primary color, you get a point. (Not Fair — there are 3 primary colors (red, blue & yellow) & 1 other color (green): 1 have a 3:4 — or 75% — chance of scoring)
  • (harder) Spin 2 4-color spinners. If the 2 colors match, Marie gets a point. If there is a mismatch, James gets a point. They felt intuitively that this wasn’t fair, but they didn’t know why. I showed them how to make a simple tree diagram. There is a 4:16 (or 1:4 or 25%) chance of getting a match and a 75% chance of a mismatch.
  • (harder) Roll two dice and multiply the numbers shown. If the product is an even number, James gets a point. If it’s an odd number, Sarah gets a point. Since an even/odd game with ONE die is clearly fair –you’d have a 3:6 chance of rolling a even number (2, 4, or 6) and a 3:6 chance of rolling an odd (1, 3 or 5) — the kids felt intuitively that this was a fair game. After they started playing they quickly changed their minds.

I asked them to fill in a square from a multiplication table showing all possible rolls in this last game, coloring even and odd numbers in different colors. They quickly saw WHY it was so unfair and immediately saw the pattern. The odds are 4:16 … or 1:4 … or 25%.

Then we played around with Tootsie Roll pops. (One day it was ice cream; the next day it was lollipops. There is a pattern here).

  • If you put 4 lollipops in a bag — grape, cherry, pomegranate & chocolate — and you pull one out a random what are the chances of getting cherry? (easy — 1:4)
  • If you pull out TWO at random, what are the odds of getting a cherry AND a pomegranate? (We used a tree diagram to solve that one. The odds are 2:12 or 1:6)
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