Final answer:
To compute the probability that an event occurs at least once, you need to find the probability that the event occurs at least twice. This can be done by finding the probability that the event occurs two times plus the probability that the event occurs three times and so on. You also need to find the probability that the event occurs exactly once, more than three times, and not at all.
Step-by-step explanation:
To compute the probability that an event occurs at least once, you need to find the probability that the event occurs at least twice. This is because the complement of 'At least one event occurs' is 'No events occur.' So, if you find the probability that the event occurs at least twice and subtract it from 1, you will get the probability that the event occurs at least once (since the complement of an event is 1 minus the probability of the event occurring). For option A, you need to find the probability that the event occurs at least twice. This can be done by finding the probability that the event occurs two times plus the probability that the event occurs three times and so on. In other words, you need to find the sum of the probabilities of each individual case where the event occurs two or more times. For option B, you need to find the probability that the event occurs exactly once. This can be done by finding the probability that the event occurs one time and subtracting it from the probability that the event occurs at least twice. So you will need to find the probability that the event occurs at least twice first and then subtract the probability that the event occurs two times. For option C you need to find the probability that the event occurs more than three times. This can be done by finding the probability that the event occurs four times plus the probability that the event occurs five times and so on. In other words, you need to find the sum of the probabilities of each individual case where the event occurs four or more times.
For option D you need to find the probability that the event does not occur at all. This can be done by subtracting the probability that the event occurs at least once from 1. In other words the complement of 'At least one event occurs' is 'No events occur,' so to find the probability that the event does not occur you can subtract the probability that the event occurs at least once from 1.