First Answer:
With one six-sided die, the odds are one in two (right). With two dice, the odds are five in twelve (this is wrong).
Second Answer:
Broken down the following can be seen:
Number, Is odd?, Prime composition, Is prime?
1, Yes, 1^1, Yes
2, No, 2^1, Yes
3, Yes, 3^1, Yes
4, No, 2^2, No
5, Yes, 5^1, Yes
6, No, 3^1*2^1, No
Full disclosure however, the arguments that 1 and 2 are prime numbers are... well, debated. We'll just presume they are to simplify things (the arguments are rather complex compared to such a simple question; honestly though, I'm of the camp that believes 1 and 2 are not prime numbers, which makes the answer 2/6 for a single die).
So, the numbers that are both prime and odd are 1, 3, and 5. Really on a six sided dice you're just asking if what the probability that a number rolled is ODD will be. If this were a 16-sided die, the answer would simply follow the same logic, but be of a slightly different in nature.
The probability an odd number would be rolled is 1/2 for a single die (3/6). The probability that only one odd number would be rolled between two die is 1/2 * 1/2 (1/4). The probability that an odd number would be rolled but the other would be even (or visa versa) is still 1/2 * 1/2 (or 1/4). The probability that both are odd, or both are even is... again, 1/2 * 1/2 (or, again, 1/4). Lastly (and to answer your question), the probability that an odd number occurred at all when rolling two dice is the inverse of the probability that an odd number did not occur, which is 1 - (1/2 * 1/2) or 3/4, or 75%. If you think about it all possible combinations have been represented here. Take any given probability conjecture such as the probability that the first is odd and the second is even, because both possibilities are independently 1/2, the complement is likewise 1/2 and it makes life very, very simple when computing this.
The probability of rolling an odd number on a standard die is 3 in 6, or 1 in 2, or 0.5.
The probability of rolling an odd number is 3/6 (or rather, 1/2), so the probability of rolling an odd number three times in a row is 1/2^3 is 1/8 or 12.5%.
With a standard 6 faced die, numbered 1 through 6, there are three odd numbers, 1, 3, and 5, of which 3 and 5 are prime, and there is one even prime, 2. The probability, then, of rolling an odd number which is prime is 1 in 3, i.e. 3 or 5 out of a possible result set of 1, 2, 3, 4, 5, and 6.
The probability that, when rolling three dice none will come up odd is broken down by the probability that on odd roll will occur as an independent event. Rolling the first die has a probability of 3/6 that it will be odd. Rolling the second has the probability of 3/6 that it will be odd. Rolling the third has a probability of 3/6 will be odd. Rolling three and coming up with odd is really the probability that no odd numbers occurred, so therefore an even number DID happen (3/6), and an even number DID happen (3/6), and an even number DID happen (3/6). That's really just 1 - (3/6^3) or simplified 1 - (1/2^3). So therefore the probability that an odd number occurred in 3 die rolls is about 87.5%.
In probability questions, the word "or" means add. Assuming the numbers are 1-12, the prime numbers would be 1, 2, 3, 7, and 11. The odd numbers are 1, 3 , 5, 7, 9, and 11. You don't add duplicates when determining probability, so all your options for a prime number or an odd number are 1,2,3, 5, 7, 9, and 11. This means there are 7/12 that are prime or odd, or a probability of 0.5833.
The probability of rolling an odd number of a standard die is 3 in 6, or 1 in 2, or 0.5.
The probability for a normal die is 1/2.
There could be many questions: What is the probability of rolling an even number. What is the probability of rolling an odd number. What is the probability of rolling a number less than 4. What is the probability of rolling a number more than 3. What is the probability of rolling 1,4, or 6. Basically it could be any question about the probability of rolling half of the faces.
Odd- 3/12 ---> 1/4 Prime- 3/12 ---> 1/4 They are the same
The probability of rolling a 4 is 1/6. (There are 6 numbers one of which is "4")The probability of rolling an odd number is 3/6 = 1/2 (There are 6 numbers 3 of which are odd)Thus, in one roll of the die, the odds of rolling a 4 oran odd number = 1/6 + 3/6 = 4/6 = 2/3.
When rolling two six-sided dice, each die has three odd numbers: 1, 3, and 5. The probability of rolling an odd number on one die is 3 out of 6, or 1/2. Since the rolls are independent, the probability of rolling an odd number on both dice is (1/2) × (1/2) = 1/4, or 25%.
The probability of rolling a odd number on a standard die is 3 in 6, or 1 in 2, or 0.5.You don't say with what, so I assume with a standard six sided die. The probability of rolling an odd number with a standard six sided die is 3 in 6, or 1 in 2, or 0.5.