Two dice are rolled. What is the probability that the sum of the dots on the upward faces is NOT 12
The probability of 12 is 1/36, so the probability of NOT 12 is 1-1/36= 35/36
To find the probability that the sum of the dots on the upward faces is not 12, we need to determine the number of favorable outcomes (sum is not 12) and divide it by the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes.
To calculate the favorable outcomes, we need to find the combinations of dice rolls that result in a sum that is not 12.
There are two cases to consider:
Case 1: One of the dice shows 1 and the other dice shows any number from 2 to 6 (5 favorable outcomes).
Case 2: One of the dice shows 2 and the other dice shows any number from 1 to 5 (5 favorable outcomes).
Therefore, the total number of favorable outcomes is 5 (Case 1) + 5 (Case 2) = 10.
Step 2: Determine the total number of possible outcomes.
The two dice can each have 6 possible outcomes, so the total number of possible outcomes is 6 * 6 = 36.
Step 3: Calculate the probability.
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 10 / 36
Probability = 5 / 18
Therefore, the probability that the sum of the dots on the upward faces is not 12 is 5/18 or approximately 0.2778.
To find the probability that the sum of the dots on the upward faces is NOT 12 when two dice are rolled, we first need to determine the total number of possible outcomes.
When two dice are rolled, there are 6 possible outcomes for each die, resulting in a total of 6 × 6 = 36 possible outcomes for both dice.
Next, we need to determine the number of outcomes where the sum of the dots is 12.
Since the maximum number on a single die is 6, the only way to get a sum of 12 is to have both dice show a 6. There is only 1 outcome where both dice show 6.
Therefore, the number of outcomes where the sum of the dots is 12 is 1.
Finally, we can calculate the probability by dividing the number of desired outcomes (not getting a sum of 12) by the total number of possible outcomes.
Desired outcomes = Total outcomes - Outcomes where sum is 12
Desired outcomes = 36 - 1 = 35
Therefore, the probability that the sum of the dots on the upward faces is NOT 12 when two dice are rolled is 35/36 or approximately 0.9722.