Two dice are rolled. Find the probability of getting a sum greater than 8
To find the probability of getting a sum greater than 8 when rolling two dice, we need to determine the number of outcomes that meet the condition, as well as the total number of possible outcomes.
To begin, let's consider all the possible outcomes when rolling two dice. Each die has 6 sides, numbered from 1 to 6. So, for the first die, we have 6 possible outcomes, and for the second die, we also have 6 possible outcomes. Therefore, the total number of possible outcomes when rolling two dice is 6 x 6 = 36.
Next, let's determine the outcomes that have a sum greater than 8. The pairs of numbers that would satisfy this condition are: (3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), and (6, 6). This gives us a total of 10 outcomes.
Finally, we can calculate the probability by dividing the number of favorable outcomes (10) by the total number of possible outcomes (36):
Probability of getting a sum greater than 8 = 10/36 = 5/18 ≈ 0.278 or 27.8%
To find the probability of getting a sum greater than 8 when rolling two dice, we first need to determine the number of favorable outcomes and the total number of outcomes.
Step 1: Determine the favorable outcomes
In order to get a sum greater than 8, the only possible outcomes are:
- Rolling a 3 on the first die and a 6 on the second die
- Rolling a 4 on the first die and a 5 or 6 on the second die
- Rolling a 5 on the first die and a 4, 5, or 6 on the second die
- Rolling a 6 on the first die and a 3, 4, 5, or 6 on the second die
Hence, there are 4 favorable outcomes.
Step 2: Determine the total number of outcomes
When two dice are rolled, each die can have 6 possible outcomes. Therefore, the total number of outcomes is given by 6 x 6 = 36.
Step 3: Calculate the probability
The probability of getting a sum greater than 8 is given by:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 4 / 36
Step 4: Simplify the fraction (if necessary)
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4:
Probability = 1 / 9
Therefore, the probability of getting a sum greater than 8 when rolling two dice is 1/9.
If you take 7 minus the result of a dice throw, then that's another valid dice throw. So, for two dice throws, the probability that the sum is greater than 8, is the same as the probability of 14 minus the sum being larger than 8, which is the same as the probability of the sum being less than 6.
If we then add the probability for the sum being larger than 8 and smaller than 6, we get twice the probability. If you subtract that from 1, you get the result:
1-2 p = probablity that the sum is 6 7 or 8
where p is the desired probability.
Now the probability of the sum being 6, P(6)is the same as the sum being 8,
P(8), because 14-8 = 6, so we have:
1-2p = 2 P(6) + P(7) ------->
p = 1/2 - P(6) - 1/2 P(7)