(e) The probability that a randomly selected worker who is reported being unemployed is a college
graduate is
Pr(
𝑋𝑋
= 1
𝑌𝑌
= 0) =
Pr
(
X=1
,
Y=0
)
Pr
(
Y=0
)
=
0
.
015
0
.
068
= 0.2206
The probability that this worker is a noncollege graduate is
Pr(
𝑋𝑋
= 0
𝑌𝑌
= 0) =
Pr
(
X=0
,
Y=0
)
Pr
(
Y=0
)
=
0
.
053
0
.
068
= 0.7794
(f) Educational achievement and employment status are not independent because they do not satisfy
that, for all values of
x
and
y
,
Pr(

)
Pr(
)
Y
y X
x
Y
y
=
=
=
For example,
Pr(
𝑌𝑌
= 0
𝑋𝑋
= 0) = 0.0829
and
Pr(Y = 0) = 0.068
are different
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