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Exercise for May 23, 2009
May 1982 Part 2 Examination, Problem No. 37
An urn contains ten balls numbered 1 through 10. Five balls are drawn at random and
without replacement. Let A be the event that exactly two odd-numbered balls are drawn
and they occur on odd-numbered draws from the urn. What is the probability of event A?
A.
5
504
B.
5
252
C.
5
126
D.
5
42
E.
25
63
Solution.
The event A is the union of the following three events:
{Odd, Even, Odd, Even, Even},
{Odd, Even, Even, Even, Odd},
{Even, Even, Odd, Even, Odd}.
Therefore, the probability sought is
5 5 4 4 3 5 5 4 3 4 5 4 5 3 4
5
⋅ ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ =
.
10 9 8 7 6 10 9 8 7 6 10 9 8 7 6 42
Answer D.
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