Suppose events A and B are assumed to be independent, but when calculated, P(A and B)
eq P(A) × P(B). What does this suggest?

Question

Suppose events A and B are assumed to be independent, but when calculated, P(A and B) 
eq P(A) × P(B). What does this suggest?

BlackTom AI · Accepted Answer

We start by parsing the scenario: A and B are assumed independent, yet the calculated P(A and B) does not equal P(A) × P(B). 
Option 1: 'The events are conditional' — This would imply that A and B depend on each other in some way. If P(A and B) ≠ P(A)P(B), that is evidence against independence, which aligns with the idea of dependence rather than a conditional relationship being the default interpretation. So this option is not supported by the given contradiction alone. 
Option 2: 'The events are still independent' — This directly contradicts the given fact that P(A and B) ≠ P(A) × P(B). Since the fundamental property of independence is precisely P(A and B) = P(A)P(B), the mismatch shows they are not independent. Therefore, this option is incorrect. 
Option 3: 'There is not enough information' — The statement P(A and B) ≠ P(A) × P(B) provides a specific mathematical discrepancy that is sufficient to conclude dependence. Therefore, this option is not accurate given the evidence provided. 
Option 4: 'The events are not independent' — This is the correct interpretation of the discrepancy. If the product of the marginals does not equal the joint probability, independence does not hold, so the events are not independent. 
In summary, options 1 and 3 are unsupported by the given inconsistency, option 2 directly contradicts the observed result, and option 4 correctly reflects what P(A and B) ≠ P(A) × P(B) implies about the relationship between A and B.

ETX5900 - S2 2025 In-workshop quiz week 3

Suppose events A and B are assumed to be independent, but when calculated, P(A and B) \neq P(A) × P(B). What does this suggest?

查看解析

登录即可查看完整答案

类似问题

Are the event that a student chooses the finance option and the event that she chooses the co-op stream independent?

True / False: If two events are mutually exclusive, they must also be independent.

Suppose events A and B are assumed to be independent, but when calculated, P(A and B) \neq P(A) × P(B). What does this suggest?

Suppose a person is chosen at random. Use your understanding about football to decide whether the event that the person weighs more than 300 pounds and the event that the person plays professional football are independent or associated.

Suppose a person is chosen at random. Use your understanding about football to decide whether the event that the person weighs more than 300 pounds and the event that the person plays professional football are independent or associated.

Expected co-occurrences for events A and B (computed under the assumption that the two events are independent) are largely different from observed co-occurrences for these two events. What conclusion can you make? Choose one best answer:

True or False. All independent events are disjoint.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单