If two dice are rolled, what is the probability that the sum of the numbers is at least 8?
Well, when it comes to rolling dice, the probability can be quite a roll of the dice itself! But fear not, I'll entertain you with an answer.
Let's see... there are 6 possible outcomes for each of the two dice, giving us a total of 6 x 6 = 36 possible outcomes when both dice are rolled.
Now, we need to figure out all the combinations that give us a sum of at least 8. The combinations that work are: (2,6), (3,5), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5), and (6,6).
So, that makes 14 favorable outcomes.
Therefore, the probability of getting a sum of at least 8 is 14/36, which simplifies to 7/18.
So, grab your dice and give it a roll, but remember, no matter the outcome, laughter is always the best probability booster!
To find the probability that the sum of the numbers rolled on two dice is at least 8, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
Total number of possible outcomes:
When two dice are rolled, each die can have 6 possible outcomes. So, the total number of possible outcomes is 6 * 6 = 36.
Number of favorable outcomes:
To determine the number of favorable outcomes, we need to find the combinations of dice rolls that result in a sum of at least 8. These combinations are:
(2, 6), (3, 5), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), and (6, 6).
Counting these favorable outcomes, we find that there are 14 combinations.
Probability of the sum being at least 8:
The probability is calculated as favorable outcomes divided by total outcomes.
So, the probability is 14/36, which simplifies to 7/18 or approximately 0.389.
Therefore, the probability that the sum of the numbers rolled on two dice is at least 8 is 7/18 or approximately 0.389.
To calculate the probability that the sum of the numbers on two dice is at least 8, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Total number of outcomes when two dice are rolled:
When you roll a single six-sided die, there are 6 possible outcomes (numbers 1-6). Since we are rolling two dice, the total number of possible outcomes will be 6 * 6 = 36.
Favorable outcomes:
To find the favorable outcomes, we need to determine the pairs of numbers on two dice that sum up to at least 8. These pairs are:
(2, 6), (3, 5), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).
So, there are 14 favorable outcomes.
Probability:
The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the probability is:
P(sum of numbers is at least 8) = Number of favorable outcomes / Total number of outcomes
= 14 / 36
= 7 / 18
Therefore, the probability that the sum of the numbers on two dice is at least 8 is 7/18 or approximately 0.3889.
1/36
There are 36 possibilities in rolling two dice. To get 8 or more ("at least 8"), you will need:
3, 5
3, 6
6, 3
5, 3
4, 4
4, 5
4, 6
5, 4
6, 4
5, 5
5, 6
6, 5
6, 6
Can you figure it out from there?