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Probabilistic Models for Dynamical Systems, 2nd Edition
book

Probabilistic Models for Dynamical Systems, 2nd Edition

by Haym Benaroya, Seon Mi Han, Mark Nagurka
May 2013
Intermediate to advanced content levelIntermediate to advanced
764 pages
6h 43m
English
CRC Press
Content preview from Probabilistic Models for Dynamical Systems, 2nd Edition
2.26. Continuing Example 2.17, let G be the event of rolling a 3 and A
1,
A
2
, A
3
be the events of selecting
die 1, 2, or 3, respectively.
(a) Find the probability of rolling a 3 if one die is selected at random. Use the theorem of total probability.
(b) Determine the probability that die 2 was chosen if a 3 was rolled with the randomly selected die.
Solution: It is given that G is an event of rolling a 3 and A
1
, A
2
, A
3
equal the event of selecting die 1,2,
or 3, respectively.
(a) Since the die is selected at random,
Pr(A
1
) = Pr(A
2
) = Pr(A
3
) = 1/3.
From the table,
Pr(G|A
1
) = 1/12, Pr(G|A
2
) = 1/6, Pr(G|A
3
) = 1/6.
Substituting these into the total probabilit ...
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Publisher Resources

ISBN: 9781439849897