Two 6-sided dice are rolled. Find the odds of rolling s sum that is a prime number
Possible prime sums are 2,3,5,7, and 11
number of ways to get 2 = 1
numbr of ways to get 3 = 2
number of ways to get 5 = 4
number of ways to get 7 = 6
number of ways to get 11 = 2
total = 15
prob of that happening = 15/36 = 5/12
so prob of that NOT happening = 1-5/12 = 7/12
odds in favour of a sum which is prime = (5/12) : (7/12)
= 5 : 7
To find the odds of rolling a sum that is a prime number when two 6-sided dice are rolled, we first need to determine the favorable outcomes and the total number of possible outcomes.
A sum is considered a prime number if it can only be evenly divided by 1 and itself, meaning it cannot be divided by any other number.
Let's list all the possible outcomes when two 6-sided dice are rolled:
Dice 1 | Dice 2 | Sum
---------------------
1 | 1 | 2
1 | 2 | 3
1 | 3 | 4
1 | 4 | 5
1 | 5 | 6
1 | 6 | 7
2 | 1 | 3
2 | 2 | 4
2 | 3 | 5
2 | 4 | 6
2 | 5 | 7
2 | 6 | 8
3 | 1 | 4
3 | 2 | 5
3 | 3 | 6
3 | 4 | 7
3 | 5 | 8
3 | 6 | 9
4 | 1 | 5
4 | 2 | 6
4 | 3 | 7
4 | 4 | 8
4 | 5 | 9
4 | 6 | 10
5 | 1 | 6
5 | 2 | 7
5 | 3 | 8
5 | 4 | 9
5 | 5 | 10
5 | 6 | 11
6 | 1 | 7
6 | 2 | 8
6 | 3 | 9
6 | 4 | 10
6 | 5 | 11
6 | 6 | 12
Out of these possible outcomes, we need to identify the sums that are prime numbers. As we can see, the following sums are prime numbers: 2, 3, 5, 7, 11.
Therefore, there are 5 favorable outcomes.
Since there are 36 possible outcomes (since each dice has 6 possible outcomes), the odds of rolling a sum that is a prime number is 5/36.
Note: The odds can also be expressed as a probability by dividing the favorable outcomes by the total number of outcomes: 5/36 ≈ 0.1389 or approximately 13.89%.