Let the sample space of dice $1$ and dice $2$ be $\text{S}_{1}$ and $\text{S}_{2}$ respectively.
- ${\color{Blue}{\text{S}_{1} = \{\text{Q, R, S, T, U, V}\} = 6}}$
- ${\color{Purple}{\text{S}_{2} = \{\text{Q, R, S, T, U, V}\} = 6}}$
The two dice are thrown once independently at random.
In probability, two events are ${\color{Magenta}{\text{independent}}}$ if the incidence of one event does not affect the probability of the other event. If the incidence of one event does affect the probability of the other event, then the events are ${\color{Red}{\text{dependent}}}$.
- Two events $\text{A}$ and $\text{B}$ are ${\color{Magenta}{\text{independent}}}$ if:
- $\text{P} (\text{A} \cap \text{B}) = \text{P(A)} \cdot \text{P(B)}$
The probability that the outcomes on the dice were composed only of any combination of the following possible outcomes$: \text{Q, U},$ and $\text{V} = \frac{3}{6} \times \frac{3}{6} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}.$
Correct Answer $:\text{A}$