PSTAT 120A, Spring 2010, Practice Midterm.
1. In a closet there are 10 pairs of shoes. If six shoes are selected at
random, what is the probability of
a) no complete pairs;
b) exactly one complete pair;
c) exactly two complete pairs;
d) exactly three complete pairs?
2. Suppose that a convention organizer assigns each guest to stay in one
of three hotels: labelled hotel B, C and D respectively.
Suppose that
10 % of guests are assigned to stay in hotel B;
30 % of guests are assigned to stay in hotel C; and
60 % of guests are assigned to stay in hotel D.
Suppose that this ﬁlls up all the rooms in each of the three hotels.
Suppose that 10 % of the rooms in hotel B have internet access;
suppose that 30 % of the rooms in hotel C have internet access; and
suppose that 5 % of the rooms in hotel D have internet access.
Suppose that a guest is randomly selected. Let
A
represent the event
that they were assigned to stay in a room with internet access.
(a) Find the probability of event
A
.
(b) Suppose that a conference guest is randomly selected, and that
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 Spring '10
 RohiniKumar
 Logic, Probability, Inductive Reasoning, Randomness, Internet access, complete pairs, hotel D. Suppose

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