Question

analyzing a claim

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(\text{nf}|\text{pb}) = p(\text{nf})\\)
• yes, the two events are independent because \\(p(\text{pb}|\text{nf}) = p(\text{nf})\\)
• no, the two events are not independent because \\(p(\text{pb}|\text{nf}) \

eq p(\text{pb})\\)

• no, the two events are not independent because \\(p(\text{pb}|\text{nf}) \

eq p(\text{nf})\\)

Explanation:

Calculate the probabilities from the table

Using the Two-Way Frequency Tables and Conditional Probability Calculation knowledge points

$$
LATEXBLOCK0
$$

Determine independence and evaluate the claim

Using the Independent Events knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) Yes, the two events are independent because \(P(\text{NF}\mid\text{PB}) = P(\text{NF})\) (Correct answer)
• (B) Yes, the two events are independent because \(P(\text{PB}\mid\text{NF}) = P(\text{NF})\)
• (C) No, the two events are not independent because \(P(\text{PB}\mid\text{NF})

eq P(\text{PB})\)

• (D) No, the two events are not independent because \(P(\text{PB}\mid\text{NF})

eq P(\text{NF})\)