Problem Solving for CGS Statistics Students
Six problems are outlined below. One problem must be handed in to your math teacher. A grading rubric will be used to score your solution. Please consult this rubric to ensure you are handing in a complete and thoughtful solution. The honor code is to be followed in completing this assignment. Here are the problems to choose from:
#1
An expert gives team
A only a 40% chance to win the World Series.
Basing his calculations on this, a gambler offers 6 to 5 odds on team B
to win the first game? Is his
judgment sound? Explain
#2 In the country of Puevigi, the population consists of Soothsayers, who never lie, Dissemblers, who always lie, and Diplomats, who alternately lie and tell the truth. If you meet a citizen of Puevigi, how with just two questions can you determine to which group he belongs?
#3 Two cylindrical
cans have the same volume. The
height of one can is triple the height of the other.
If the radius of the narrower can is 12 units, how many units are in the
length of the radius of the wider can? Express
your answer in simplest radical form
©NCTM
#4 If the eggs in a basket are removed two at a time, one egg will remain. If the eggs are removed three at a time, two eggs will remain. If the eggs are removed four, five, or six at a time, then three, four and five eggs will remain, respectively. If they are taken out seven at a time, however, no eggs will be left over. Find the smallest number of eggs that could be in the basket.
©Crossing the River with Dogs
#5 Martian coins are 3 sided (heads, tails and torsos), each side coming up with equal probability. Three Martians decided to go odd-man-out to determine who pays a dinner check. (If two coins come up the same and one different, the owner of the latter coin foots the bill). What is the expected number of throws needed in order to determine a loser?
#6 If a,b,c and d are real numbers, what is the
numerical value of the sum
3x3 - 8x2
+7 is written in the form
©Mathematics League