There is a 25% chance that a book has a red cover, a 32% chance that a book is fiction, and a 16% chance that a book is fiction with a red cover. Determine whether the events "red cover" and "fiction" are approximately independent events. Justify mathematically.

Approximately independent, because 16% = 25% + 32%
Not independent, because 16% ≠ 25% + 32%
Approximately independent, because 16% = (25%)(32%)
Not independent, because 16% ≠ (25%)(32%)

Question

There is a 25% chance that a book has a red cover, a 32% chance that a book is fiction, and a 16% chance that a book is fiction with a red cover. Determine whether the events "red cover" and "fiction" are approximately independent events. Justify mathematically.

Approximately independent, because 16% = 25% + 32%
 Not independent, because 16% ≠ 25% + 32%
 Approximately independent, because 16% = (25%)(32%)
 Not independent, because 16% ≠ (25%)(32%)

toga · Answer

The answer is d. "Not independent, because 16% ≠ (25%)(32%)".

To determine if the events "red cover" and "fiction" are independent, we can use the formula P(A and B) = P(A) * P(B), where A and B are events.

Let A be the event that a book has a red cover, and B be the event that a book is fiction. We are given that:
- P(A) = 25%
- P(B) = 32%
- P(A and B) = 16%

If A and B are independent events, then P(A and B) = P(A) * P(B). 
Substituting the given probabilities, we get:
16% = (25%)*(32%)

However, this is not true, since 16% is not equal to (25%)*(32%). Therefore, we can conclude that the events "red cover" and "fiction" are not independent.