Math 221
Week 4 Lab
Submitted by:
Major Walker
Part 1.
CrossReference Tables and Probability
1.
What is the probability that the cereal would be high calorie? In other
words, what is P(high calorie)?
a.
=
Phigh calorie
number of high calorie cerealstotal
=
= .
number of cerials
5384
0 6310
2.
What is the probability that the cereal would be high fiber? In other words,
what is P(high fiber)?
a.
=
Phigh fiber
number of high fiber cerealstotal number
=
=
= .
of cerials
2284
1142
0 2619
3.
What is the probability that a cereal would both high calorie and high
fiber? In other words, what is P(high calorie and high fiber)?
a.
=
Phigh calorie and high fiber
number of high calorie
and high fiber cerealstotal number of
=
=
= .
cerials
1884
314
0 2143
b.
4.
What is the probability that a cereal would either high calorie or high
fiber? In other words, what is P(high calorie or high fiber)?
a.
=
+

Phigh calorie or high fiber
Phigh calorie Phigh fiber
=
+

Phigh calorie and high fiber
5384 2284
=
=
= .
1884
5784
1928
0 6786
5.
What is the probability that a cereal would be high calorie, given that it is
high fiber? In other words, what is P(high calorie, given high fiber)?
a.
=
Phigh caloriehigh fiber
Phigh calorie and high
=
/
/
=
=
= .
fiberPhigh fiber
18 8422 84
1822
911
0 8182
b.
6.
What is the probability that a cereal would be high calorie, given that is is
low fiber?
In other words, what is P(high calorie, given low fiber)?
a.
=
Phigh calorielow fiber
Phigh calorie and low fiberPlow
=
/
/
=
=
= .
fiber
12 8433 84
1233
411
0 3636
7.
Regarding Questions 5 and 6, how might you interpret this information as
a consumer?
a.
If a high fiber cereal is randomly selected, the probability that is a high
calorie cereal is 0.8182. If a low fiber cereal is randomly selected, the
probability that it is a high calorie cereal is 0.3636. So a high fiber
cereal is most probably a high calorie cereal also.
8.
Using the simple test of independence (described in the lecture), decide if
the events high calorie and high fiber are independent or dependent. Show
your work.
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a.
The events “high calorie’ and “ high fiber” are independent if and only
if
=
×
Phigh calorie and high fiber
Phigh calorie
Phigh
fiber
b.
= .
Phigh calorie and high fiber
0 2143
c.
×
= .
×
= .
Phigh calorie
Phigh fiber
0 6310
2619
0 1652
d.
The condition of independence is not satisfied. The events are not
independent.
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 Spring '11
 novick
 Statistics, Probability, Trigraph, high fiber, high calorie, high calorie cereal

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