Two dice are rolled. Find the probability of getting a sum greater than 8.
0
13/36
2/9
5/18
2x=
5/18
To find the probability of getting a sum greater than 8 when two dice are rolled, you need to determine the number of possible outcomes that result in a sum greater than 8 and divide it by the total number of possible outcomes.
There are a total of 36 possible outcomes when two dice are rolled, because each die has 6 possible outcomes (numbers 1 to 6) and the total number of outcomes is the product of the number of outcomes on each die (6 * 6 = 36).
Now let's find the number of possible outcomes with a sum greater than 8:
- If the first die shows a 1, then the second die needs to show a number greater than 7 - which is not possible. So, no outcomes from this case.
- If the first die shows a 2, then the second die needs to show a number greater than 6 - which is also not possible. No outcomes from this case either.
- If the first die shows a 3, then the second die needs to show a number greater than 5 - only 1 outcome satisfies this condition: (3, 6).
- If the first die shows a 4, then the second die can show any number from 3 to 6 - a total of 4 outcomes: (4, 3), (4, 4), (4, 5), (4, 6).
- If the first die shows a 5, then the second die can show any number from 2 to 6 - a total of 5 outcomes: (5, 2), (5, 3), (5, 4), (5, 5), (5, 6).
- If the first die shows a 6, then the second die can show any number from 1 to 6 - a total of 6 outcomes: (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).
Adding up the outcomes from all cases gives us a total of 16 favorable outcomes.
Now, divide the number of favorable outcomes (16) by the total number of possible outcomes (36):
P(sum > 8) = Favorable outcomes / Total outcomes = 16 / 36 = 4 / 9
So, the correct answer is 4/9.