Question

there is a 25% chance that a book has a red cover, a 32% chance that a book is fiction, and an 8% chance that a book is fiction with a red cover. determine whether the events
ed cover\ and \fiction\ are approximately independent events. justify mathematically.
approximately independent, because 8% = (25%)(32%)
not independent, because 8% ≠ 25% + 32%
approximately independent, because 8% = (25%)(32%)
not independent, because 8% = (25%)(32%)

Explanation:

Step1: Recall the formula for independent events

If two events \(A\) and \(B\) are independent, then \(P(A\cap B)=P(A)\times P(B)\). Let event \(A\) be “red - cover” with \(P(A) = 25\%=0.25\), and event \(B\) be “fiction” with \(P(B)=32\% = 0.32\). Then \(P(A)\times P(B)=0.25\times0.32 = 0.08=8\%\).

Answer:

Approximately independent, because \(8\%=(25\%)(32\%)\)