Final answer:
The probability of rolling a 4, 5, 1, or 3 on a six-sided die is 0.6667 and the odds against such an event are 1:2. The odds against an event are calculated as the ratio of the number of unfavorable outcomes to the number of favorable outcomes.
Step-by-step explanation:
The subject of the question asked by the student is Mathematics, specifically related to the topic of probability using a six-sided die. Within this context, the odds against rolling a 4, 5, 1, or 3 on a fair six-sided die revolves around a basic understanding of probability and outcomes.
Since the die used is fair, each side has an equal chance of landing face-up. With six sides on the die and the desired outcomes being 4, 5, 1, or 3, we have a total of four favorable outcomes out of six possible outcomes when the die is rolled once. Therefore, the probability of rolling a 4, 5, 1, or 3 is 4/6 or 2/3. Expressing this as a decimal rounded to four decimal places gives us 0.6667.
The odds against an event are calculated as the ratio of the number of unfavorable outcomes to the number of favorable outcomes. In this case, there are two unfavorable outcomes (rolling a 2 or a 6) and four favorable outcomes (rolling a 4, 5, 1, or 3). Therefore, the odds against rolling a 4, 5, 1, or 3 are 2:4, which simplifies to 1:2. This means for every instance of not rolling a 4, 5, 1, or 3, there are two instances where you would roll one of these numbers.