On Thu, 6 Nov 2003, jim clark wrote: > Hi > > On 6 Nov 2003, Curious George wrote: > > > [EMAIL PROTECTED] (Curious George) wrote in message > > news:<[EMAIL PROTECTED]>... > > > I am an instructor, using 'Elementary Statistics: A Brief > > > Version, 2/e' by > > > Allan G. Bluman. A questions in the database states: > > > > > > A family has three children. How many combinations of boys and > > > girls will be in the sample space? > > > > > > The answer given is: 8. > > > _______________________________ > > > > > > Even if you allow for 'birth order' I can not identify more than 6 > > > possible outcomes. Am I missing something?
Yes, evidently; though it's hard to say what, since you didn't enumerate the six. The following may help, if you haven't thought of it this way already: Either there are 3 boys, or 2 boys and a girl, or a boy and 2 girls, or 3 girls. If there are 2 boys, the girl may be the youngest, the middle, or the eldest child; and similarly if there is one boy he maybe youngest, middle, or eldest. That brings you to 8: 1 (all boys) + 3 (2 boys) + 3 (2 girls) + 1 (all girls). Enumerated in birth order, the 8 possibilities are: BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG. This is all easily related to Pascal's triangle if you get into binomial computations, as Jim suggests. -- DFB. > > > Thanks, > > > George > > > > "I see, said the blind man....." I needed to reverse the birth order. > > George > > Depending on what you plan to do later (e.g., binomial), you > might want to teach this as a general principle based on the > multiplication rule. That is, 2 outcomes (BG) on each of 3 > trials gives > > 2 x 2 x 2 = 2^3 = 8 > > and then relate this to the enumeration and/or a tree diagram of > the outcomes. > > Best wishes > Jim ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
