## Monday, April 23, 2012

### An Equal Number of Democrats and Republicans Are Locked In a Room

An equal number of Democrats and Republicans are locked in a room (at least 2 of each).  If 2 are released at random, what is the probability that there will be one from each party? Remember,  your answer must be both mathematically and politically correct.

(a) What questions should your students ask before starting the problem? And if they don't..
(b) Is it worthwhile to give students 10 sec to make an intuitive guess?
(c) Do you think 1/2 will be intuitively guessed by a majority?
(d) What strategies do you want your students to use with an open-ended question like this?
(e) Would you have your students solve problem if there were originally 2 from each party, then, say, 3 from each?
(f) Show that if there are originally n from each party, the desired probability is n/(2n-1).
(g) As n increases beyond all bound...
(h) What do you see as the benefits of this inquiry?
(i) How would you extend this investigation?  (j) How would you have done it differently depending with middle schoolers vs secondary?
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