Final answer:
The probability that the total showing when two fair dice are rolled is either even or less than nine is 3/4.
Step-by-step explanation:
To find the probability that the total showing when two fair dice are rolled is either even or less than nine, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
Let's consider the event of the total showing being even. Outcomes that satisfy this event are (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), and (6,6). That means there are 9 favorable outcomes for event A.
Now let's consider the event of the total showing being less than nine. All the outcomes listed above (9 outcomes) satisfy this event, along with the outcomes (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (3,1), (4,1), (5,1), and (6,1). That means there are 18 favorable outcomes for event B.
To calculate the probability, we can add the number of favorable outcomes for both events (9 + 18 = 27) and divide it by the total number of possible outcomes when rolling two dice, which is 36.
The probability that the total showing is either even or less than nine is therefore 27/36, or 3/4.