Final answer:
The probability of throwing a three or a five on a single roll of a fair six-sided die is 1/3. This is calculated by adding the individual probabilities of rolling a three and a five, which are both 1/6, resulting in a total probability of 2/6, or simplified to 1/3.
Step-by-step explanation:
The question is asking for the probability of obtaining a three or a five when a fair six-sided die is thrown once. To find this probability, consider the possible outcomes when rolling a die, which are 1, 2, 3, 4, 5, and 6. Out of these, the favorable outcomes for the event described - rolling a three or a five - are just two numbers: 3 and 5.
The probability of any one outcome on a six-sided die is 1/6, since all outcomes are equally likely and there are six possible outcomes. Therefore, to find the probability of rolling either a three or a five, you add the probabilities of each individual outcome:
- Probability of rolling a three (P(3)): 1/6
- Probability of rolling a five (P(5)): 1/6
Since these are separate and non-overlapping events, their probabilities can be added together:
P(3 or 5) = P(3) + P(5) = 1/6 + 1/6 = 2/6 or 1/3 when simplified.
The probability of throwing a three or a five on a single roll of a fair six-sided die is therefore 1/3.