Q&A #3784

Tree diagram: Four Children (2B's/2G's any order)

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From: Judy Bellonio
To: Teacher2Teacher Service
Date: Apr 24, 2000 at 18:27:36
Subject: Tree diagram: Four Children (2B's/2G's any order)

I am teaching my students how to make a tree diagram.  The problem that I
will be discussing is the probability of a particular sequence of boys and
girls when there are four children.  I know that the probability of having a
boy 1st is 1/2, of having a girl last is 1/2, of having four boys is 1/16,
of having four girls is 1/16 and I understand the formulas associated with
these.  The problem that I can not get the formula for is the probability of
having two boys and two girls in any order.  I know the answer is 6/16 by
using a tree diagram.  My question is, is there a mathematical formula to
figure this out?

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