Math 300 , Spring 2004, Day 6, F, Feb 13 Hit
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I am not here, but you are:
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Check all assigned problems, pool your knowledge. I would guess
that at least one person will find Ash p. 34, # 7 less than
crystal clear. Do all you can to clarify.
Someone email me what problems you still have questions on.
sievers@wells.edu
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Work as a group, or in pairs. Choose which interests you most
first. I doubt you'll get them all. Write up what you get
and leave it in the Math 300 box outside my door.
A1) Remember Ann and Xavier? Suppose there are 4 girls and
3 boys, and Ann and Xavier don't want to sit next to each other.
If all are assigned at random to 7 chairs in a row, GBGBGBG, find the
number of ways that A and X are NOT together? Assuming all the
children are distinguishable/ have names. (I think assigning
Xavier first is the nicest approach.) Generalize to n boys and
n+1 girls.
What is the probability that A and X are not together, if the
assignment is made at random?
A2) Now suppose there are an even number of boys and girls, still
sitting alternately. Assume BGBG...Boy first. What are the
number of ways that Ann and Xavier
are not together? (I know how to do A1; I haven't thought about
A2). Start with small numbers, see if you can generalize to n of
each. The probability they are not together?
B) 
Suppose I have a cardboard
circle whose diameter is half the length of one of the square
tiles on the classroom floor.
The experiment is to toss the circle on the floor. What is the
probability that the circle lands wholly within a square (not touching
the sides)?
Assume that any place on the floor is as likely as any other
place. Hint: Think about where the center of the circle
lands, do the geometry using that.
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