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Unformatted text preview: aw of total
probability uses terms of the form P (A|Ei ). In many instances, as illustrated in the following
examples, the values P (A|Ei ) are speciﬁed by the probability model, and (2.13) or (2.14) are used
for calculating P (Ei |A).
Example 2.10.1 There are three dice in a bag. One has one red face, another has two red faces,
and the third has three red faces. One of the dice is drawn at random from the bag, each die having
an equal chance of being drawn. The selected die is repeatedly rolled.
(a) What is the probability that red shows on the ﬁrst roll?
(b) Given that red shows on the ﬁrst roll, what is the conditional probability that red shows on
the second roll?
(c) Given that red shows on the ﬁrst three rolls, what is the conditional probability that the selected
die has red on three faces? 2.10. THE LAW OF TOTAL PROBABILITY, AND BAYES FORMULA 49 Solution: Let Ei be the event that the die with i red faces is drawn from the bag, for i =1, 2, or
3. Let Rj denote the event that red shows on the j th role of the die.
(a) By the law of total pr...
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- Spring '08
- The Land