Final answer:
The theoretical probability of an event not occurring is found by subtracting the probability of the event from 1. If the event's probability is 5/7, then the probability of the event not occurring is 2/7.
Step-by-step explanation:
The question is about calculating the theoretical probability of an event not occurring. If the theoretical probability of an event occurring is 5/7, the probability of the event not occurring is found by subtracting this probability from 1. So, the theoretical probability of the event not occurring is 1 minus 5/7, which equals 2/7.
To explain this further, in probability theory, the probability of all possible events in a sample space adds up to 1. Therefore, if we know the probability of an event happening, we can find the probability of it not happening by subtracting the event's probability from 1. For instance, when you roll a fair six-sided die, the probability of rolling a 7 is 0 since 7 is not on any face of the die. Using similar logic, if the probability of an event (like rolling at least a five) is 2/6, the probability of not rolling at least a five is 4/6 or 2/3.