Two dice are rolled, what is the probability of getting a” sum of at least 5”?
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.
To find the probability of getting a sum of at least 5 when two dice are rolled, we can calculate the probability of the complementary event (i.e., the event where the sum is less than 5) and subtract it from 1.
To determine the probability of getting a sum less than 5, we need to consider the favorable outcomes and the total possible outcomes.
1. Determine the favorable outcomes:
- The possible combinations of dice rolls that give a sum less than 5 are:
- (1, 1), (1, 2), (2, 1), (1, 3), (3, 1), (2, 2)
So there are 6 favorable outcomes.
2. Determine the total possible outcomes:
- When two dice are rolled, there are 6 possible outcomes for each dice (from 1 to 6). Since we are rolling two dice, the total possible outcomes would be 6 x 6 = 36.
3. Calculate the probability of getting a sum less than 5:
- Probability = (Number of favorable outcomes) / (Total possible outcomes)
= 6 / 36
= 1 / 6
4. Calculate the probability of getting a sum of at least 5:
- Probability = 1 - Probability of getting a sum less than 5
= 1 - 1/6
= 5/6
So, the probability of getting a sum of at least 5 when two dice are rolled is 5/6.