Two 6-sided fair dice are rolled. What is the probability that the sum of the two numbers on the dice will not be 9?
To find the probability that the sum of the numbers on two 6-sided dice will not be 9, we need to find the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Determine the favorable outcomes
The sum of two dice will be 9 if and only if one die shows a 3 and the other shows a 6, or vice versa (6 + 3 or 3 + 6). There are two possible ways this can happen.
Step 2: Determine the total number of outcomes
Each die has 6 possible outcomes. Since we are rolling two dice, the total number of outcomes is 6 x 6 = 36.
Step 3: Calculate the probability
The probability is the number of favorable outcomes divided by the number of total outcomes.
Probability = Favorable outcomes / Total outcomes
Probability = 2 / 36
Probability = 1 / 18
Therefore, the probability that the sum of the two numbers on the dice will not be 9 is 1/18.
There are 4 ways to make 9, so that means
P(~9) = 32/36