Question

One fair die has faces $1, 1, 2, 2, 3, 3$ and another has faces $4, 4, 5, 5, 6, 6.$ The dice are rolled and the numbers on the top faces are added. What is the probability that the sum will be odd?

$\dfrac13$

$\dfrac49$

$\dfrac12$

$\dfrac59$

$\dfrac23$

Answer: D

Concepts:dice (probability)parity independent events

Difficulty rating: 1240

Solution:

The first die is odd (a $1$ or $3$ ) with probability $\dfrac23$ and even with probability $\dfrac13.$ The second die is odd (a $5$ ) with probability $\dfrac13$ and even with probability $\dfrac23.$

The sum is odd when the two parities differ: $\dfrac13 \cdot \dfrac13 + \dfrac23 \cdot \dfrac23 = \dfrac19 + \dfrac49 = \dfrac59.$

Thus, D is the correct answer.

2005 AMC 10B Problem 9

Answer: D

Difficulty rating: 1240

Solution:

Problem 9 in Other Years