Question

There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are equally likely. The two dice are thrown once independently at random. What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes: Q, U, and V?

• A. ( \frac{1}{4} \)
• B. ( \frac{3}{4} \)
• C. ( \frac{1}{6} \)
• D. ( \frac{5}{36} \)

Hint:

When calculating probability, determine the total number of possible outcomes and the number of favorable outcomes. Then divide the favorable outcomes by the total outcomes.

Answer 1

The Correct Option is A

Each die has 6 faces with letters Q, R, S, T, U, and V. The total number of outcomes when throwing two dice is: \[ 6 \times 6 = 36. \] Now, we are only interested in the outcomes that result in Q, U, or V on both dice. The favorable outcomes for each die can be one of the three letters: Q, U, or V. Therefore, for both dice: \[ 3 \times 3 = 9 \text{ favorable outcomes.} \] So, the probability of getting only Q, U, or V on both dice is: \[ \frac{9}{36} = \frac{1}{4}. \] Thus, the probability is \( \frac{1}{4} \).