Final answer:
The probability of rolling a die marked with numbers 1, 2, 2, 3, 3, 3 and getting a 1, a 2, and a 3 in that order is calculated using the product rule. The combined probability is found by multiplying the individual probabilities, resulting in a 1/36 chance.Option C is the correct answer.
Step-by-step explanation:
The question is asking to find the probability of rolling a die marked with numbers 1, 2, 2, 3, 3, 3 three times and getting a 1, a 2, and a 3 in that order. To solve this, we first find the probability of each event occurring separately, and then we use the product rule to find the combined probability.
The die has one face with a 1, two faces with a 2, and three faces with a 3. Therefore, the probability of rolling a 1 is 1/6, the probability of rolling a 2 is 2/6 or 1/3, and the probability of rolling a 3 is 3/6 or 1/2.
Using the product rule:
- Probability of rolling a 1: P(1) = 1/6
- Probability of rolling a 2: P(2) = 1/3
- Probability of rolling a 3: P(3) = 1/2
The combined probability of rolling a 1, then a 2, then a 3 is the product of the individual probabilities: P(1, 2, 3) = P(1) × P(2) × P(3) = (1/6) × (1/3) × (1/2) = 1/36. Hence, the correct answer is C) 1/36.