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THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT1301
Probability and Statistics I
Class Test (Makeup)
Answer all questions.
Time allowed: 1 hour
Name ______________________
Student ID _________________
Class ___________
1. [10 marks]
Suppose that a box contains one blue card without any label, and four red cards labeled
A
,
B
,
C
and
D
. Two of these five cards are selected at random, without replacement.
(a) If it is known that card
A
has been selected, what is the probability that both cards are
red?
(b) If it is known that at least one red card has been selected, what is the probability that
both cards are red?
Ans:
(a) Total number of possible outcomes of the two selected cards is
.
10
2
5
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
If card A is drawn, the combination of the two cards must be one of (A,Blue), (A,B),
(A,C), (A,D). Therefore
(
)
4
.
0
10
4
drawn
is
A
card
=
=
P
Similarly, if card A and another red card are drawn, the combination must be one out of
(A,B), (A,C), (A,D) and hence
(
)
3
.
0
10
3
drawn
is
A
card
red
cards
both
=
=
∩
P
Thus
(
)
(
)
(
)
drawn
is
A
card
drawn
is
A
card
red
cards
both
drawn
is
A
card

red
cards
both
P
P
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 Spring '08
 SMSLee
 Statistics, Probability, Probability distribution, Probability theory, Cumulative distribution function, mean residual lifetime

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