Final answer:
The probability of getting a specific sum of two dice. a) The probability of getting a sum of 1 is 1/36. b) The probability of getting a sum of 4 is 1/12. c) The probability of getting a sum less than 13 is 1.
Step-by-step explanation:
a) To find the probability that the sum of two dice is equal to 1, we need to determine the number of ways this can happen and divide it by the total number of possible outcomes. In this case, the only way to get a sum of 1 is if both dice show the number 1. Since each die has 6 possible outcomes, the total number of outcomes is 6 * 6 = 36. Therefore, the probability of getting a sum of 1 is 1/36.
b) To find the probability that the sum of two dice is equal to 4, we need to determine the number of ways this can happen and divide it by the total number of possible outcomes. The possible combinations of numbers that result in a sum of 4 are (1, 3), (2, 2), and (3, 1). Therefore, there are 3 possible outcomes that result in a sum of 4. Dividing this by the total number of outcomes (36), we get a probability of 3/36, which simplifies to 1/12.
c) To find the probability that the sum of two dice is less than 13, we have to consider that the highest possible sum is 12. Since there are no sums greater than 12, the probability of getting a sum less than 13 is 1, or 100%.