Problem

Determine whether the events $\mathrm{E}$ and $\mathrm{F}$ are independent or dependent. Justify your answer. (c) E: The unusually foggy weather in London on May 8. $\mathrm{F}$ : The number of car accidents in London on May 8. A. The number of car accidents in London on May 8 could affect the unusually foggy weather in London on May 8 , so $\mathrm{E}$ and $\mathrm{F}$ are dependent. B. The unusually foggy weather in London on May 8 could affect the number of car accidents in London on May 8, so $\mathrm{E}$ and $\mathrm{F}$ are dependent. C. The unusually foggy weather in London on May 8 could not affect the number of car accidents in London on May 8 , so $\mathrm{E}$ and $\mathrm{F}$ are independent.

Solution

Step 1 :The question is asking whether the events E and F are independent or dependent. In probability theory, two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. Conversely, two events are dependent if the occurrence of one does affect the probability of the occurrence of the other.

Step 2 :In this case, event E is the unusually foggy weather in London on May 8, and event F is the number of car accidents in London on May 8. It is reasonable to think that the weather conditions (foggy weather) could affect the number of car accidents, as foggy weather could reduce visibility and increase the likelihood of accidents. Therefore, it seems that the occurrence of event E could affect the probability of the occurrence of event F.

Step 3 :However, this is a qualitative analysis. To definitively determine whether the events are independent or dependent, we would need data on the frequency of car accidents in foggy weather versus non-foggy weather.

Step 4 :Based on the qualitative analysis, it seems that the events E and F are dependent. Therefore, the correct answer is B: The unusually foggy weather in London on May 8 could affect the number of car accidents in London on May 8, so E and F are dependent.

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Source: https://solvelyapp.com/problems/18299/

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