Final answer:
In rolling two fair 5-sided dice, there are 3 outcomes where the sum is 8 and 12 outcomes where either a 2 is rolled or the sum does not exceed 4.
Step-by-step explanation:
The question asks us to find the number of outcomes for two specific events when rolling two fair 5-sided dice. First, we identify the desirable outcomes for each event.
For the first event, where the sum of the numbers is 8, we consider all pairs of numbers (a, b) such that a+b=8 and both a and b are between 1 and 5. The outcomes are { (3,5), (4,4), (5,3) }. Thus, there are 3 outcomes for this event.
For the second event, we have two conditions: either a 2 is rolled or the sum of the dice is no more than 4. The outcomes satisfying a 2 being rolled include all pairs where at least one die is 2: { (1,2), (2,1), (2,2), (2,3), (3,2), (2,4), (4,2), (2,5), (5,2) }. The outcomes where the sum is no more than 4 are { (1,1), (1,2), (2,1), (1,3), (3,1) }. Note that the pairs with a 2 were already counted, so we only add the (1,1) and (1,3), (3,1) pairs that were not included before. Therefore, we have a total of 9 + 3 = 12 unique outcomes for the second event.