University
First Hour Exam
ECE 313
of Illinois
Summer 2003
1. (22 points)
Check the appropriate box for each statement below. Answers need not be
justified. However, in order to discourage guessing, you will be penalized for wrong
answers.
(a) (10 points)
(+2 points for a correct answer,
−
2 points for a wrong answer, and 0 points
for no answer) Which of the following statements are true for all events A and B such that 0
< P(A) < 1, 0 < P(B) < 1?
TRUE
FALSE
P(A  B ) > P(A)
P(A  B) + P(A  B
c
) = 1
P(A  B) + P(A
c
 B) = 1
P(B  A) P(A) + P(A  B
c
) P(B
c
) = P(A)
P(A  B) = P(B  A) P(B)/P(A)
(b) (12 points)
(+12 points for a correct answer,
−
3 points for a wrong answer, and 0 points
for no answer) Which of the following four statements are true for all events A and B such
that 0 < P(A) < 1, 0 < P(B) < 1?
(a) P(A
∩
B)
≤
min{P(A), P(B)}
(b) P(A
∪
B)
≥
[P(A) + P(B)]
/
2
(c) P(A
∩
B)
≥
P(A) + P(B)
−
1
(d) P(A
∩
B)
≤
P(A  B)
Only
(a) and (c) are true statements.
Only
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 Spring '09
 NegarKayavash
 Probability theory, Following, Discrete probability distribution

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