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MA 316: MATHEMATICAL PROBABILITY
ASSIGNMENT #2: SOLUTIONS: SECTION 1.4
FALL 2003
1.34: For part a), notice that the event in which the colors alternate occurs only if we choose from the
bowl either RBRB or BRBR in these orders. Since the probability of the ﬁrst outcome is
3
8
5
7
2
6
4
5
and the
probability of the second outcome is
5
8
3
7
4
6
2
5
, then the probability of the desired event is the sum of these
values which is 1
/
7. For part b), notice that the only way in which we can obtain the ﬁrst blue chip on the
third draw is if we choose from the bowl RRB in that order, and this event has probability
3
8
2
7
5
6
=
5
56
.
1.35: If
B
denotes the event in which we are dealt at least 3 kings in our hand of 13 cards and
A
the
event we are dealt at least two kings, then we are asked to compute the conditional probability
P
(
B

A
) =
P
(
A
∩
B
)
/P
(
A
) =
P
(
B
)
/P
(
A
)
.
Since
P
(
B
) =
£(
4
3
)(
48
10
)
+
(
4
4
)(
48
9
)/
(
52
13
)
and
P
(
A
) =
£(
4
2
)(
48
11
)
+
(
4
3
)(
48
10
)
+
(
4
4
)(
48
9
)/
(
52
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This note was uploaded on 09/10/2009 for the course STATS 517 taught by Professor Song during the Fall '07 term at Purdue UniversityWest Lafayette.
 Fall '07
 Song
 Probability

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