2008 AMC 10B Problem 20

The faces of a cubical die are marked with the numbers

1,

2,

2,

3,

3,

and

4.

The faces of a second cubical die are marked with the numbers

1,

3,

4,

5,

6,

and

8.

Both dice are thrown. What is the probability that the sum of the two top numbers will be

5,

7,

9?

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Solution

Of the

36

equally likely outcomes, the pairs giving sum

5

are

(1,4),(2,3),(2,3),(4,1),

which is

4

outcomes. Sum

7

comes from

(1,6),(2,5),(2,5),

(3,4),(3,4),(4,3),

which is

6,

and sum

9

from

(1,8),(3,6),(3,6),(4,5),

which is

4.

The probability is

\tfrac{4+6+4}{36}=\tfrac{14}{36}=\tfrac{7}{18}.

Thus, the correct answer is B.