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AMS131: Introduction to Probability Theory (Spring 2008)
Quiz 1 Solutions
1. (6 points). Assume that the probability that student
A
will fail a certain mathematics examina
tion is 0
.
5; the probability that student
B
will fail the same examination is 0
.
2; and the probability
that both student
A
and
B
will fail the examination is 0
.
1.
(a) What is the probability that neither student
A
nor student
B
will fail the examination?
Solution:
Let
A
and
B
be the events that student
A
and
B
, respectively, will fail the examination.
It is given that Pr(
A
) = 0
.
5; Pr(
B
) = 0
.
2; and Pr(
A
∩
B
) = 0
.
1. The event that “neither student
A
nor student
B
will fail the examination” can be expressed as
A
c
∩
B
c
; its probability can be computed
as follows, Pr(
A
c
∩
B
c
) = Pr
{
(
A
∪
B
)
c
}
= 1

Pr(
A
∪
B
) = 1

(Pr(
A
) + Pr(
B
)

Pr(
A
∩
B
)) = 1

(0
.
5 + 0
.
2

0
.
1) = 0
.
4.
(b) What is the probability that exactly one of the two students will fail the examination?
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 Spring '08
 Kottas

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