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Unformatted text preview: iDate: 10/16/11
gTime: 5:55 PM
1 Ln.“ __. .. W. Course: Math 201 Fall B10 Book: Larson: Elementary Statistics:
Picturing the World, 5e Assignment: Week 3 Exercises The table below shows the results oﬁa survey in which 145 families were asked if they own a computer and if
they will be taking a summer vacation this year. Own
a Summer Vacation This Year '3 Yes _
Yes 46
No 55 Computer Total 101 No
10
34
44 Total
56'
89 145 The empirical probability of an event E is the relative frequency of event E. P(E) = (a) Find the probability that a randomly selected family is not taking a summer vacation this year. First ﬁnd f, the number of families that are not taking a summer vacation this year. f: 44 Now ﬁnd n, the total number of families surveyed. n= 145 Frequency of event E Total frequency ii
11 Using the empirical probability formula, find the probability P(N) where N is the event of not taking a summer Vacation. pm) (b) Find the probability that a randomly selected family owns a computer. ll 44
145
0303‘ (Round to the nearest thousandth as needed.) 56 of 145 families own a computer. Using the empirical probability formula, ﬁnd the probability P( C) where C is the event of owning a computer. P(C) ll 56
145
.386 (Round to the nearest thousandth as needed.) Page 1 g l
E Ass1gnment Week 3 Exercises ]
lDate: 10/16/11 Course: Math 01 Fall B10 l
l lTime: 5:55 PM Book: Larson: Elementary Statistics:
[ Picturing the World, Se (c) Find the probability a randomly selected family is taking a summer vacation this year given that they own a
Computer. A conditional probability is the probability of an event occurring, given that another event has already occurred. From part (b), the number of families owning a computer is 56. 46 of them are taking a summer vacation this
year. ' . Let V be the event of taking a summer vacation. Using the empirical probability formula ﬁnd P(VI C), the probability a randomly selected family is taking a
summer vacation this year given that they own a computer 46
NW C) = g. = .821 (Round to the nearest thousandth as needed.) ((1) Find the probability a randomly selected family is taking a summer vacation this year and owns a computer.
The probability that two events C and V will occur in sequence is found using the multiplication rule.
P(C and V) I P(C) P(Vl C) Using the multiplication rule, ﬁnd the probability a randomly selected family is taking a summer vacation this
year and owns a computer. 5—6 4—6
P(C and V) : 1—45 56
46
2 E
: .317
/ (Round to the nearest thousandth as needed.) (e) Are the events of owning a computer and taking a summer vacation this year independent or dependent
events? ‘ Two events are independent if the occurrence of one of the events does not affect the probability of the
occurrence of the other event. The condition of independence of two events C and V is the following. NW C) : P(V) Assignment: Week 3 Exercises Date: 10/16/11 Course: Math 201 Fall B10
Time: 5:55 PM Book: Larson: Elementary Statistics:
i Picturing the World, Se 101 of 145 families are taking a summer vacation this year. . Using the empirical probability formula, ﬁnd P(V) , the probability of taking a vacation. 101
145 2 0.697‘ ' (Round to the nearest thousandth as needed.) P(V). : Recall from part (c) that P(VI C) = 0.821. As P(VI C) i P(V), the events of owning a computer and taking a
summer vacation this year are dependent. ' YOU ANSWERED: .3034
.696 Page 3 ...
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