A three-sided die is described as fair, meaning each outcome is equally likely. Thus, each outcome $R, S, P$ has the same probability.

The total number of outcomes is $3$ (one for each of $R, S, P$), and each outcome has an equal likelihood:

$\text{Pr(outcome)} = \frac{1}{\text{total outcomes}} = \frac{1}{3}.$

Probability distribution:

a) $\text{Pr}(R) = \frac{1}{3}$
b) $\text{Pr}(S) = \frac{1}{3}$
c) $\text{Pr}(P) = \frac{1}{3}$

Would you like me to explain further or provide a visualization of the probabilities?

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Here are 5 related questions to deepen understanding:

1. What is the sum of probabilities for all outcomes in any probability distribution?
2. If the die were unfair, how would the probabilities of $R, S, P$ change?
3. How would the probabilities change if there were 4 equally likely outcomes instead of 3?
4. What is the probability of rolling $R$ or $S$ on this die?
5. How would you simulate rolling a fair three-sided die using a standard six-sided die?

Tip: Always verify that the total probability sums up to $1$, ensuring your distribution is valid.