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?

The correct option is 1/4.

To find the probability that the outcomes on both dice are composed only of a combination of the letters Q, U, and V, we can break down the problem step-by-step.

Step 1: Determine the total number of possible outcomes
Each of the two identical dice has 6 faces, labeled with the letters: Q, R, S, T, U, and V.
Since the two dice are thrown independently, the total number of possible outcomes when both are rolled is:
Total outcomes = 6 × 6 = 36

Step 2: Determine the number of favorable outcomes
We want the outcomes on both dice to consist only of the letters Q, U, or V.
This means for each individual die, the outcome must be one of these 3 letters (Q, U, or V).
The number of favorable choices for the first die is 3 (Q, U, or V).
The number of favorable choices for the second die is also 3 (Q, U, or V).
Since the dice are thrown independently, the total number of favorable combinations is:
Favorable outcomes = 3 × 3 = 9

Step 3: Calculate the probability
The probability is the ratio of the number of favorable outcomes to the total number of possible outcomes:

$$\text{Probability}=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}=\frac{9}{36}=\frac{1}{4}$$

Thus, the probability that the outcomes are composed only of Q, U, and V is 1/4.