Final answer:
To find the odds against an event with a probability of 4/7, we calculate the probability that the event does not occur, which is 3/7, giving us odds against the event of 3:4.
Step-by-step explanation:
The question asks to find the odds against an event where the probability of the event occurring is 4/7. The probability is the ratio of the favorable outcomes to the total outcomes. To find the odds against the event, we look at the ratio of the unfavorable outcomes to the favorable outcomes. The total of all probabilities is 1 (or 7/7), so the probability of the event not occurring (odds against) is 1 minus the probability of the event, which results in 3/7.
Therefore, the odds against the event are the number of ways the event can not occur to the number of ways the event can occur, which is 3:4. In other words, for every 3 times the event does not occur, it occurs 4 times.