Which of the following events has a theoretical probability equal to $\frac{1}{3}$?

• A. Flipping a fair coin and getting heads
• B. Drawing a heart from a standard deck of cards
• C. Rolling a fair six-sided die and getting a multiple of $3$
• D. Rolling a fair six-sided die and getting a number less than $3$

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the concept of theoretical probability, which is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. The formula is: \(\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\).
2. Step 2: Analyze each event to determine the number of favorable outcomes and total outcomes. For example, a fair six-sided die has 6 possible outcomes: {1, 2, 3, 4, 5, 6}.
3. Step 3: Calculate the probability for the event 'Rolling a fair six-sided die and getting a multiple of 3'. The favorable outcomes are {3, 6}, so the number of favorable outcomes is 2. The total outcomes are 6. Thus, the probability is \(\frac{2}{6}\).
4. Step 4: Simplify the fraction \(\frac{2}{6}\) to its lowest terms to check if it equals \(\frac{1}{3}\).
5. Step 5: Repeat the same process for the other events (flipping a coin, drawing a heart, rolling less than 3) and compare their probabilities to \(\frac{1}{3}\) to confirm which event matches the theoretical probability of \(\frac{1}{3}\).