Question

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 $5,$ $7,$ or $9?$

$\dfrac{5}{18}$

$\dfrac{7}{18}$

$\dfrac{11}{18}$

$\dfrac{3}{4}$

$\dfrac{8}{9}$

Answer: B

Concepts:dice (probability)systematic listing

Difficulty rating: 1510

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.

2008 AMC 10B Problem 20

Answer: B

Difficulty rating: 1510

Solution:

Problem 20 in Other Years