Problem Set 5  not to be turned in
Problem 1
An experiment consists of drawing balls
without replacement
from an urn containing 10 balls
numbered 1
,
2
,...,
10.
For each of the following statements, answer True if the statement is
always
true, and answer
False otherwise. If you answered True, provide a brief argument (e.g., you can cite a theorem
proved in class or in a book.). If you answered False, provide the correct answer. It is ﬁne to leave
answers containing factorials, combinations and permutations as they are without evaluating
them.
(a) For
E,F
∈ F
,
P(
E
∩
F
c
) = P(
E
)

P(
E
∩
F
).
(b) Let
E
n
be the event that ball number 1 is still in the urn after the
n
th
draw, 1
6
n
6
10.
Then,
E
n
is an increasing sequence of events.
(c) The total number of diﬀerent orders in which these 10 balls can be drawn is 10
10
.
(d) The probability that we get ball number 1 in the very ﬁrst draw is
1
10
.
(e) The probability that we get ball number 1 in exactly the fourth draw is
1
10
.
(f) After four balls are drawn, the probability that the minimum numbered ball being the
fourth is 1
/
(
10
4
)
.
(g) Suppose we distribute these balls among three diﬀerent urns, urn 1, urn 2 and urn 3. There
are
(
10
3
)
possible diﬀerent arrangements.
(h) Suppose each ball is placed in one of the three urns, urn 1, urn 2 or urn 3 randomly with
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 Spring '08
 Staff
 Probability theory

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