A single die is rolled once. What are the odds against rolling a prime number?
2, 3 and 5 would be considered prime, which mean that 1, 4 and 6 are non-prime. The die has 6 sides.
You should be able to work it out with that information.
To determine the odds against rolling a prime number with a single die, we first need to understand the concept of prime numbers. Prime numbers are integers greater than 1 that are only divisible by 1 and themselves.
A standard die has six sides numbered from 1 to 6. To find the odds against rolling a prime number, we need to identify the total number of favorable outcomes (rolling a non-prime number) and the total number of possible outcomes (all numbers on the die).
Step 1: Determine the favorable outcomes (non-prime numbers)
Prime numbers on a standard die are 2, 3, and 5. Therefore, the favorable outcomes are rolling a 1, 4, or 6, which are non-prime numbers.
Step 2: Determine the total possible outcomes
Since there are six sides on a die, there are six possible outcomes when it is rolled.
Step 3: Calculate the odds against rolling a prime number
The odds against an event (rolling a prime number, in this case) can be expressed as the ratio of favorable outcomes to unfavorable outcomes.
Favorable outcomes: Rolling a 1, 4, or 6 (3 outcomes)
Total possible outcomes: All numbers on the die (6 outcomes)
The odds against rolling a prime number are 3 to 6, or simply 1 to 2. This means that for every one favorable outcome, there are two unfavorable outcomes.
Note: It's important to note that the probability of rolling a prime number is different from the odds against rolling a prime number. Probability is the measure of how likely an event is to occur, while odds are a ratio that compares the likelihood of an event to its non-occurrence.