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.

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?Multiple choice

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