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Hit
.01
E
1
= HH
Hit
?
Miss
E
2
= HM
.09
E
3
= MH
Hit
Miss
.81
Miss
E
4
= MM
Economics 70 Book Exercise 2
Exercise Title: Book Exercise 2Error: Reference source not found
Date: 11:52:36
Name (Last, First): ANSWER KEY
PID:
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3.1
This experiment involves tossing a single die and observing the outcome.
The sample space for
this experiment consists of the following simple events:
E
1
: Observe a 1
E
4
: Observe a 4
E
2
: Observe a 2
E
5
: Observe a 5
E
3
: Observe a 3
E
6
: Observe a 6
A through F are compound events and are composed in the following manner:
A: (E
2
)
D: Contains no simple events
B: (E
1
, E
3
, E
5
)
E: (E
1
, E
2
, E
3
, E
5
)
C: (E
1
, E
2
, E
3
)
F: (E
2
)
To find the probability of an event, we sum the probabilities assigned to the simple events in that
event.
Since the simple events are equally likely, P(E
i
) = 1/6
for
i
= 1,.
.6, so that
P(A) = 1/6
P(B) = 3/6 = ½
P(C) = 3/6 = ½
P(D) = 0
P(E) = 4/6 = 2/3
P(F) = P(E
2
) = 1/6
2.
The assignment of probabilities is valid in this experiment, since each probability lies between 0
and 1 and since the sum of the four probabilities equals 1.
3.3.
In order to have a valid assignment of probabilities, we must have
Since P(E
1
) + P(E
2
) + P(E
3
) + P(E
4
) = 4(.15) = .6, we must have P(E
5
) = 1  .6 = .4.
3.4
It is given that P(E
1
) = P(E
2
) = .15 and P(E
3
) = .40.
Since , we know that
P(E
4
) + P(E
5
) = 1  .15  .15  .40 = .30
(
i
)
Also, it is given that
P(E
4
) = 2P(E
5
).
(
ii
)
1
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This note was uploaded on 04/14/2008 for the course ECON 400 taught by Professor Turchi during the Spring '08 term at UNC.
 Spring '08
 turchi
 Economics

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