A die is rolled once. What are the odds against rolling a prime number? 2
first off, what are the prime numbers?
a prime number is any number divisible by one and itself.
1, 2, 3, 5, are all prime numbers.
although 1 can be controversial. Some teachers consider 1 as a prime but some not. anyways assuming 1 is a prime. there is a total of 4 primes.
a dice has six sides of six numbers total.
so the probablility of rolling a prime number is:
4/6 and if you simplify: 2/3
but if you don't consider 1 as a prime:
the answer would be: 3/6 and simplify: 1/2
odds in favour of some event
= prob(of that event/prob(not that event)
primes form 1 to 6 are 2,3, and 5
so prob of a prime = 3/6 = 1/2
so prob of not a prime = 1-1/2 = 1/2
so the odds in favour of a non-prime = (1/2) รท (1/2)
= 1:1
Euler considered 2 to be the first prime, and who are we to argue against Euler.
yes
To determine the odds against rolling a prime number when a die is rolled once, we need to find the number of outcomes that are not prime and divide it by the total number of possible outcomes.
Step 1: Count the number of prime numbers on a standard six-sided die.
Out of the six sides of the die, there are three prime numbers: 2, 3, and 5. The prime numbers on the die are 2 and 3.
Step 2: Determine the number of outcomes that are not prime.
To find the number of outcomes that are not prime, subtract the number of prime outcomes from the total number of outcomes on a die. Since a die has six sides numbered from 1 to 6, the total number of outcomes is 6. Therefore, the number of outcomes that are not prime is 6 - 2 = 4.
Step 3: Calculate the odds against rolling a prime number.
The odds against rolling a prime number can be expressed as a ratio of the number of outcomes that are not prime to the number of outcomes that are prime.
The odds against rolling a prime number are 4 to 2, or 4:2. This can be simplified further by dividing both sides by the greatest common divisor (which is 2 in this case) to obtain 2:1.
Therefore, the odds against rolling a prime number when a die is rolled once are 2 to 1.