Final answer:
The probability that neither die shows a five is 1/18 (approximately 0.056).
The probability of getting a sum less than ten is 5/9 (approximately 0.556).
Step-by-step explanation:
a) To find the probability that neither die shows a five, we need to determine the number of favorable outcomes and the total number of possible outcomes.
There are 2 ways for neither die to show a five (for example, (1, 1) or (2, 2)).
The total number of possible outcomes is 6 * 6 = 36, since each die has 6 sides.
So, the probability is 2/36 = 1/18 (approximately 0.056).
b) To find the probability of getting a sum less than ten, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The possible sums less than ten are 2, 3, 4, 5, 6, 7, 8, and 9.
There are 20 ways to achieve these sums, which can be calculated by listing all the possible combinations or using a table.
The total number of possible outcomes is 6 * 6 = 36.
So, the probability is 20/36 = 5/9 (approximately 0.556).