Final answer:
The probability that all three randomly chosen neighbors hate you is calculated by multiplying the individual probabilities of selecting a neighbor who hates you consecutively, which comes down to (44/55) * (43/54) * (42/53).
Step-by-step explanation:
The question is asking for the probability that if you meet 3 of your neighbors randomly, all of them hate you. Given that 44 out of 55 neighbors hate you, we can find this probability by using the concept of combinations without replacement from probability theory. The steps to calculate this are as follows:
1. First, calculate the probability of selecting a neighbor who hates you on the first try. This is 44/55.
2. Next, for the second neighbor chosen, there are now 54 neighbors to choose from, and 43 who hate you, so the probability is 43/54.
3. Finally, for the third neighbor, there are 53 neighbors left, with 42 hating you, yielding a probability of 42/53.
4. Multiply all these probabilities together to get the final probability that all three randomly chosen neighbors hate you: (44/55) * (43/54) * (42/53).
When you calculate these numbers, you get the final probability for the event in question.