Final answer:
The probability of rolling a number that is either a multiple of 3 or a prime number on a six-sided die is 2/3.
Step-by-step explanation:
When rolling a six-sided die, the sample space S is {1, 2, 3, 4, 5, 6}. To find the probability of rolling a number that is either a multiple of 3 or a prime number, we first identify the numbers on the die that meet the criteria. The multiples of 3 are {3, 6} and the prime numbers are {2, 3, 5}. Therefore, combining these, we get the numbers {2, 3, 5, 6}. There are four desired outcomes out of six possible outcomes when rolling the die once.
The probability formula is P(E) = number of favorable outcomes / total number of possible outcomes. Substituting the values, we get P(E) = 4/6, which can be simplified to 2/3. Hence, the probability of rolling a number that is either a multiple of 3 or a prime number on a six-sided die is 2/3 or approximately 0.667.