MAT271H1 Midterm: Sample test solution
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1) A bag contains a large number of marbles, one-quarter of them red, the rest blue. Six marbles are drawn
at random. What is the probability that exactly 2 of them are red?
(6 choose 2)*(1/4)^2*(3/4)^4
2) (i) Why do we not have to worry about being engulfed in yogurt?
Bacteria in yogurt reproduce and the yogurt grows exponentially. Theoretically it would engulf the
entire world;however, the calculation assumes that they have enough food to reproduce at a constant
rate forever, and in reality there isn’t enough food for the bacteria,therefore this situation would
(ii)Why do we not have to worry that the number of people infected with the H1N1pandemic will grow
exponentially until the whole country is sick?
Exactly the same as the yogurt question,except in this case the “food” for the bacteria is the number
of people that are susceptible to the virus. Every individual has different DNA and therefore
different vulnerability to the virus. Therefore, when the number of susceptible people is reduced, the
virus slows down and eventually stops.
3) Moose have been mentioned three timesin this course. Describe the contexts in which they have arisen.
Moose 1: brahe's pet: Tycho Brahe made detailed measurements of the positions of the planets over a
long period of time. His pet moose died after drinking too much beer and felt down a flight stairs.
Moose 2: irish elk example, showed in calculations of regression lines that their antler is huge
compared to their body size (increases as the body gets bigger).
Moose 3: genetics newfoundland
4) Explain the advantages and disadvantages of Mercator's projector and describe how he got in trouble
with the authorities.
Mercator's projector was good for local navigation because angles were preserved but the distances
change at different latitudes (i.e Canada looks even bigger than it actually is). The maps are so good
for short-range navigation, but not so good for long-range navigation. They also cannot extend as far
as the poles: to do so they would require an infinitely large map. Mercator fell under suspicious of
heresy, mostly because he travelled widely to gather information for his maps.
(** Mercator’s projection draws the lines of longitude as parallel lines, instead of letting them get closer
together as they are near the poles. In effect, the horizontal scale increases the vertical scale the farther
it is from the equator.)
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