Two dice are rolled. What are the odds in favor of a sum less than 5?
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1/36
To find the odds in favor of a sum less than 5 when two dice are rolled, we first need to determine the favorable outcomes and the total number of possible outcomes.
Favorable outcomes:
The possible sums less than 5 when rolling two dice are:
- Sum of 2: (1,1)
- Sum of 3: (1,2), (2,1)
- Sum of 4: (1,3), (2,2), (3,1)
So, there are 6 favorable outcomes in total.
Total number of possible outcomes:
When rolling two dice, each die has 6 possible outcomes (numbers from 1 to 6). Since there are two dice, the total number of possible outcomes is 6 x 6 = 36.
Therefore, there are 6 favorable outcomes and 36 possible outcomes.
To calculate the odds in favor, we divide the number of favorable outcomes by the number of possible outcomes:
Odds in favor = Favorable outcomes / Total possible outcomes
Odds in favor = 6 / 36 = 1 / 6
Hence, the odds in favor of a sum less than 5 when two dice are rolled is 1/6.
To find the odds in favor of a sum less than 5 when two dice are rolled, we first need to determine the different ways the sum can be less than 5.
Let's analyze the possible outcomes:
1. If both dice show a value of 1, the sum will be 2.
2. If one die shows a value of 1 and the other shows a value of 2, the sum will be 3.
3. If one die shows a value of 2 and the other shows a value of 1, the sum will also be 3.
4. If one die shows a value of 1 and the other shows a value of 3, the sum will be 4.
5. If one die shows a value of 3 and the other shows a value of 1, the sum will also be 4.
6. If one die shows a value of 2 and the other shows a value of 2, the sum will be 4.
7. If one die shows a value of 1 and the other shows a value of 4, the sum will be 5.
8. If one die shows a value of 4 and the other shows a value of 1, the sum will also be 5.
9. If one die shows a value of 2 and the other shows a value of 3, the sum will be 5.
10. If one die shows a value of 3 and the other shows a value of 2, the sum will also be 5.
So, there are 10 possible outcomes where the sum is less than 5.
To calculate the odds in favor, we need to divide the number of favorable outcomes (10) by the total number of possible outcomes when rolling two dice.
Each die has six faces, numbered 1 to 6. Therefore, the total number of outcomes when rolling two dice is 6 * 6 = 36.
Dividing the number of favorable outcomes (10) by the total number of possible outcomes (36) gives us:
Odds in favor = 10/36
This can be simplified by dividing both numerator and denominator by their greatest common divisor (which is 2 in this case):
Odds in favor = 5/18
Therefore, the odds in favor of a sum less than 5 when two dice are rolled is 5 to 18.