answer:To find the probability of flipping 7 heads in a row using a single coin, we consider the probability of getting a head in a single flip and then extend it to 7 consecutive flips. The probability of getting a head in a single flip of a fair coin is 1/2. Since each flip is independent of the others, the probability of getting a head in the next flip remains the same, 1/2. To find the probability of getting 7 heads in a row, we multiply the probability of getting a head in each individual flip together, because each flip is an independent event. This means we need to calculate (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2). This can be simplified to (1/2)^7. Calculating this gives us 1/128. Therefore, the probability of flipping 7 heads in a row using a single coin is 1/128.

answer:At first glance, it might seem that the outcome of the 8th flip should influence the probability of the first 7 flips being heads, but this is not the case. Each coin flip is an independent event, meaning the outcome of one flip does not affect the outcome of another. Given that the probability for any single flip is 50%, or 1/2, the probability of the first 7 flips being heads remains (1/2)^7, as we calculated earlier, which equals 1/128. The 8th flip, being a head, does not provide any new information about the first 7 flips because the flips are independent. The outcome of the 8th flip does not change the probability of the first 7 flips being all heads; it merely adds another independent event with its own probability. Therefore, the probability that the first 7 coin flips are all heads, given that the 8th flip was also a head, remains 1/128. This demonstrates a fundamental aspect of probability theory: when events are independent, the occurrence of one event does not affect the probability of the others.

answer:Here's the edited paragraph with explanations: They're coming to the store terribly fast. I replaced The there with They're because They're is a contraction of they are, which is the correct subject-verb combination in this sentence. I also changed therible to terribly, which is the correct adverb to describe the verb coming. Additionally, I replaced too with to, as to is the correct preposition to indicate direction, whereas too is an adverb meaning also. The manager is really scared. I changed realy to really, which is the correct adverb to describe the verb is. This is a common spelling mistake, and using the correct spelling ensures that the sentence conveys the intended meaning. The business has been losing a lot of money because of the competition from across the street. I replaced buisness with business, which is the correct spelling of the noun. I also changed loosing to losing, as losing is the correct verb to describe the act of something being lost or decreasing. Additionally, I replaced alot with a lot, which is the correct phrase to describe a large quantity. I changed becuse to because, which is the correct subordinating conjunction to introduce the reason for the action. Finally, I replaced acrost with across, which is the correct preposition to describe the location. The new store there has better deals than us. I changed ther to there, which is the correct adverb to describe the location. I also replaced beter with better, which is the correct comparative form of the adjective good. Additionally, I changed then to than, which is the correct conjunction to introduce a comparison. Note, however, that the sentence could be improved further by using the subject-verb agreement correctly; a more grammatically correct version would be The new store there has better deals than we do.

answer:To convey the intended meaning, you could rephrase the sentence to: They're coming after us terribly fast. However, this still might not clearly convey the original intended meaning. A more precise rephrasing would be: The competition from across the street is catching up with us terribly fast. Or, to make it more concise and idiomatic: The store across the street is closing in on us fast. Alternatively, you could use a more business-oriented phrase: The competition from across the street is gaining ground on us rapidly. These rephrased sentences aim to capture the original intended meaning that the store across the street is rapidly gaining an advantage over the speaker's store.