Final Answer:
(a) The probability of rolling a prime number on a standard six-sided die is 1/2.
(b) The probability of rolling a multiple of 3 on a standard six-sided die is 1/2.
Step-by-step explanation:
(a) A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. On a standard six-sided die, the prime numbers are 2, 3, and 5. There are three prime numbers out of the six possible outcomes, so the probability of rolling a prime number is the number of favorable outcomes (3) divided by the total possible outcomes (6), which simplifies to 1/2.
(b) A multiple of 3 is a number that can be evenly divided by 3. On a standard six-sided die, the multiples of 3 are 3 and 6. There are two multiples of 3 out of the six possible outcomes, so the probability of rolling a multiple of 3 is the number of favorable outcomes (2) divided by the total possible outcomes (6), which also simplifies to 1/2.
In summary, both probabilities are 1/2, indicating that the events of rolling a prime number or a multiple of 3 on a standard six-sided die are equally likely. The calculations align with the fundamental principles of probability and the basic properties of a standard six-sided die.