STAT/MA 416
August 22, 2011
Problem Set 1
Name:
1. Choosing points at random.
(a.)
A point is chosen at random inside in the triangle in Figure 1.
What is the sample
space? [Please give mathematical expression(s), rather than just (
x, y
) is “in the triangle”.]
x
y
0
1
2
1
2
Figure 1: A triangle.
(b.) A point is chosen at random in the quadrilateral in Figure 2. What is the sample space?
[Hint: It might be helpful to give bounds on the
x
coordinate and then give bounds on the
y
coordinate.]
x
y
0
1
2
3
4
1
2
Figure 2: A quadrilateral.
1
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2. Socks.
A matching pair of blue socks, a matching pair of red socks, and one lone white
rightfooted sock are in a drawer. The socks are pulled out of the drawer, one at a time.
Suppose the color and the “foot” of the sock are both noted as all five socks are consec
utively pulled out of the drawer. Then, for instance, a possible outcome is:
(“blue right”, “white right”, “red left”, “red right”, “blue left”)
.
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 Fall '08
 Staff
 Probability, Howard Staunton

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