There are 36 possible outcomes when rolling two dice. To find the probability of getting a sum of at least 5, we can count the number of outcomes that have a sum of 5, 6, 7, 8, 9, 10, 11, or 12.
Sum of 5: There is only one way to get a sum of 5, by rolling a 1 and a 4 or a 2 and a 3, both of which are equally likely. Therefore, there are 2 outcomes that result in a sum of 5.
Sum of 6: There are two ways to get a sum of 6, by rolling a 1 and a 5, a 2 and a 4, or a 3 and a 3. Therefore, there are 3 outcomes that result in a sum of 6.
Sum of 7: There are three ways to get a sum of 7, by rolling a 1 and a 6, a 2 and a 5, a 3 and a 4, or a 4 and a 3. Therefore, there are 4 outcomes that result in a sum of 7.
Sum of 8: There are four ways to get a sum of 8, by rolling a 2 and a 6, a 3 and a 5, a 4 and a 4, a 5 and a 3, or a 6 and a 2. Therefore, there are 5 outcomes that result in a sum of 8.
Sum of 9: There are four ways to get a sum of 9, by rolling a 3 and a 6, a 4 and a 5, a 5 and a 4, or a 6 and a 3. Therefore, there are 4 outcomes that result in a sum of 9.
Sum of 10: There are three ways to get a sum of 10, by rolling a 4 and a 6, a 5 and a 5, or a 6 and a 4. Therefore, there are 3 outcomes that result in a sum of 10.
Sum of 11: There are two ways to get a sum of 11, by rolling a 5 and a 6 or a 6 and a 5, both of which are equally likely. Therefore, there are 2 outcomes that result in a sum of 11.
Sum of 12: There is only one way to get a sum of 12, by rolling two sixes, which is equally likely to any other outcome. Therefore, there is 1 outcome that results in a sum of 12.
Adding up all the outcomes that result in a sum of at least 5, we get:
2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 24
Therefore, the probability of getting a sum of at least 5 when rolling two dice is:
24/36 = 2/3 or approximately 0.667.
So, the probability of getting a sum of at least 5 when rolling two dice is 2/3 or approximately 0.667.
Two dice are rolled, what is the probability of getting a” sum of at least 5”?
1 answer