Class Openers

Class Opener – Day 7 – Probability Fail

Today’s opener comes from the site Math-Fail, which I use often for quick visuals and discussion starters.  This particular post is called Probability Fail:


There was quite a buzz in my room as students discussed whether this question was “real”, or one of my tricks (aside – they seem to be wise to my style by this point – always be skeptical!). But I have no reason to believe the task is anything but authentic, unfortunately. To see what they thought, I had the class answer the question and assessed their thoughts by a show of hands:

How many of you think the answer is A?

A few tentative hands rise.

How many of you think the answer is B?

More hands, yet still uneasiness.

How many of you think this question is just plain stupid?

Many, many hands….

So, what’s the problem with this question? I was thrilled that the first student to volunteer refered to “independence” – that coins don’t talk to or influence each other.  But what about those 8 heads? Is it possible that heads are “hot”, and more likely?  Or maybe tails is “due”.  Fun discussion today, which leads to a true story about a colleague I have shared many times with classes:


Our school is about 90 minutes away from Atlantic City, and when our staff was younger we would take semi-regular bus trips to the gambling mecca for a night to let off steam and enjoy some beverages together.

RouletteThis story centers around a dubious strategy for betting on roulette; in particular, using the results board to your advantage.  Here is the strategy my colleague (a highly repected and intelligent social studies teacher) provided:

  • Stand in the center of the roulette table area. Often there are 4 or 5 tables together.
  • Observe the board results. Locate a table which has had a “run” of a particular color; 4 or more of the same color.
  • Place money on the other color to win, as it is “due”
  • If you lose, repeat your bet. When you win, you will have recouped all losses and made a profit

Realizing my colleague’s strategy was full of holes, I was interested to see the theory of “run” put to the test.  We located a table where there had been 5 red results in a row. Time to make a profit!

$10 on black….spin, spin, spin…..RED!

$20 on black…spin, spin, spin…..RED!

$40 on black….spin, spin, spin…..RED!

$80 on black…spin, spin, spin…..RED!

And then we left the casino floor…$150 poorer yet with a valuable probability lesson behind us!


By Bob Lochel

HS Math Teacher. Hatboro-Horsham School District, Horsham, PA.

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