When a single six-sided die is tossed, it has six possible outcomes, which are the numbers: 1, 2, 3, 4, 5, and 6. To find the odds against rolling a number greater than 4, we first need to identify the outcomes that meet this criterion.
The numbers greater than 4 on a die are 5 and 6. Thus, there are 2 favorable outcomes (rolling a 5 or a 6) when rolling a number greater than 4.
Now, we need to determine the total number of outcomes. Since there are 6 faces on a die, the total number of possible outcomes is 6.
The odds against an event are calculated by taking the ratio of the number of unfavorable outcomes to the number of favorable outcomes. In this case, the unfavorable outcomes are rolling a 1, 2, 3, or 4, which gives us 4 unfavorable outcomes.
Thus, the odds against rolling a number greater than 4 can be calculated as follows:
Odds Against = Unfavorable Outcomes : Favorable Outcomes
Odds Against = 4 : 2
We can simplify this ratio by dividing both sides by 2, which gives us:
Odds Against = 2 : 1
Therefore, the odds against rolling a number greater than 4 on a tossed die are 2 to 1.