Final answer:
To find the odds against rolling a 4, 5, 1, or 3 with a six-sided die, we consider that there are four favorable outcomes out of six possible outcomes. The odds against the event are the ratio of unfavorable outcomes (rolling a 2 or 6) to favorable outcomes (rolling a 1, 3, 4, or 5), giving us odds of 1 to 2.
Step-by-step explanation:
The question asks us to find the odds against rolling a 4, a 5, a 1, or a 3 with a fair six-sided die. To calculate this, we first determine the probability of the event occurring, and then use it to find the odds against the event.
Let's define our sample space, S, which is {1, 2, 3, 4, 5, 6} for a six-sided die. The mentioned event includes rolling a 1, 3, 4, or 5. This gives us four favorable outcomes. The total number of outcomes is six since there are six sides on the die.
Probability of rolling a 1, 3, 4, or 5 is calculated by the number of favorable outcomes divided by the total number of outcomes:
P(Event) = Favorable Outcomes / Total Outcomes = 4 / 6
Since odds against is given as the ratio of the probability of the event not happening to the probability of the event happening, we need to consider the outcomes where a 2 or 6 is rolled, which are two in number.
The odds against rolling a 1, 3, 4, or 5 would thus be:
Odds Against = Unfavorable Outcomes / Favorable Outcomes = 2 / 4 = 1 / 2
Therefore, the odds against rolling a 1, 3, 4, or 5 on a six-sided die are 1 to 2.