
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 ...