1
Homework 3 (15 points)
due Feb. 3.
(1 pt.) 2.42. A commuter train arrives punctually at a station every half hour. Each
morning, a commuter named John leaves his house and casually strolls to the strain
station. Find the probability that John waits for the train
a) between 10 and 15 minutes.
Since the commuter train leaves every 30 minutes, the maximum wait time is less than 30
minutes. This is equivalent to using geometric probability over the interval [0,30). Note: I am
defining my interval as the wait times. The interval could also be defined as the time that John
arrives at the station.
? ?±??
????
²?????³
10
±³´
15
??³µ??¶·
=
¸¹
10,15
º¸
¸¹
0,30
·¸
=
5
30
=
1
6
= 0.167
b) at least 10 minutes.
? ?±??
????
»?
±?
¼?±¶?
10
??³¶·
=
¸¹
10,30
·¸
¸¹
0,30
·¸
=
20
30
=
2
3
= 0.667
(2 pt.) 2.44ab. A point is chosen at random in the unit square
= {(x,y)
: 0
x
1, 0
y
1}. Describe each of the following events in words and determine the probability of
each.
a) A = {(x,y)
: x > 1/3}
The event that the x coordinate is greater than 1/3 exclusive, the y coordinate is between 0 and
1.
? ½·
=

¾?¿?±³?¼?
²?????³
À
= 0,
À
= 1,
Á
=
1
3
,
Á
= 1)

µ³??
¶Âµ±¾?

=
1
∙
2/3
1
=
2
3
= 0.667
b) B = {(x,y)
: y
0.7}
The event that the y coordinate is less than 0.7 inclusive, the x coordinate is between 0 and 1.
? Ã·
=

¾?¿?±³?¼?
²?????³
À
= 0,
À
= 0.7,
Á
= 0,
Á
= 1)

µ³??
¶Âµ±¾?

=
1
∙
0.7
1
= 0.7
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(1.4 pts.) 2.50. According to the
National Vital Statistics Report
, there were 4,058,814 live
births in the United States in 2000. Of those births, 3,194,005 were to white mothers and
622,598 were to black mothers.
a) Use the data to obtain the approximate probability that a live birth in the United States
is to a white mother, black mother, otherrace mother.
? °????
?±???²³
=
3194005
4058814
= 0.787,
? ´µ?¶·
?±???²³
=
622598
4058814
= 0.153
? ¸???²
¹?¶?
?±???²³
=
4058814
−
3194005
−
622598
4058814
=
242211
4058814
= 0.060
OR
P(Other Race mother) = 1.000 – 0.787 – 0.153 = 0.0060
b) What type of probabilities did you obtain in part (a)? Explain.
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 Spring '08
 Staff
 Probability, Probability theory, personal lives, Jc Pc, Republican lawyer

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