the two - way table shows the distribution of book style to genre. miguel claims that given that the book is…

the two - way table shows the distribution of book style to genre. miguel claims that given that the book is paperback (pb) does not affect the outcome that the book is nonfiction (nf). is miguels claim correct? yes, the two events are independent because p(nf|pb)=p(nf). yes, the two events are independent because p(pb|nf)=p(nf). no, the two events are not independent because p(pb|nf)≠p(pb). no, the two events are not independent because p(pb|nf)≠p(nf).\nfiction nonfiction total\npaperback 20 60 80\nhardcover 10 30 40\ntotal 30 90 120

the two - way table shows the distribution of book style to genre. miguel claims that given that the book is paperback (pb) does not affect the outcome that the book is nonfiction (nf). is miguels claim correct? yes, the two events are independent because p(nf|pb)=p(nf). yes, the two events are independent because p(pb|nf)=p(nf). no, the two events are not independent because p(pb|nf)≠p(pb). no, the two events are not independent because p(pb|nf)≠p(nf).\nfiction nonfiction total\npaperback 20 60 80\nhardcover 10 30 40\ntotal 30 90 120

Answer

Answer:

Yes, the two events are independent because $P(NF|PB)=P(NF)$.

Explanation:

Step1: Calculate $P(NF)$

$P(NF)=\frac{90}{120}=\frac{3}{4}$

Step2: Calculate $P(NF|PB)$

$P(NF|PB)=\frac{60}{80}=\frac{3}{4}$

Step3: Compare probabilities

Since $P(NF|PB) = P(NF)=\frac{3}{4}$, the two events are independent.