Stat
201
Exam
2
Spring
2008
Version 3 KEY
Page
1
of
9
1.
In the United States, 12% of the population is black; while in Britain, only 1
.
6% of the
population is black.
this is P(X) this is P(Y)
Suppose you randomly select two people: One from the U.S., and one from Britain.
Let
X
represent the event ‘the American is black’.
Let
Y
represent the event ‘the Brit is black.’
Remark: This exercise was anticipated by exercises 1 and 2 on the practice exam; it is
just like scenario 3 of lab 6 and exercise 1 of lecture 12; the ideas were covered in various
exercises of homework 6, and throughout lectures 10, 11, and 12.
(a)
Are the two events disjoint? Circle the best answer:
[3 pts]
(i) Yes, because 12%
1
.
6%
(ii) No, because 12%
1
.
6%
(iii) Yes, because both people could be black.
(iv) No, because both people could be black.
(v) Yes, because each person is selected from a different country.
(vi) No, because each person is selected from a different country.
(b)
Are the two events independent? Circle the best answer:
[3 pts]
(i) Yes, because 12%
1
.
6%
(ii) No, because 12%
1
.
6%
(iii) Yes, because both people could be black.
(iv) No, because both people could be black.
(v) Yes, because each person is selected from a different country.
(vi) No, because each person is selected from a different country.
Regardless of what you select from the
U.S., the chance of getting a black Brit is
still 1.6%
Symbolically, P(Y given X) = P(Y)
(c)
Suppose that you first look at the American, but not yet at the Brit. If you find
that the American is black, then,
given
that fact, which of the following is most
reasonably the probability that the Brit will then be black?
[3 pts]
P(Y given X) = P(Y), because
the events are independent
(i)
zero
(iv)
.
136
(ii)
.
12
(v)
.
13408
(iii)
.
016
(vi) close to 100%