Question

which of the following is true if the given tree diagram represents independent events? a. the probability of buying a hardcover is less than buying a paperback. b. the probability of buying fiction versus nonfiction is not the same regardless of whether or not the person buys a hardcover or paperback. c. the probability of buying fiction versus nonfiction is the same regardless of whether or not the person buys a hardcover or paperback. d. the probability of buying nonfiction is larger than buying fiction.

Explanation:

Step1: Analyze probability of hard - cover and paperback

The probability of buying a hard - cover is $P(\text{hard - cover})=0.35$, and the probability of buying a paperback is $P(\text{paperback}) = 0.65$. Since $0.35<0.65$, the probability of buying a hard - cover is less than buying a paperback.

Step2: Analyze probability of fiction and non - fiction given hard - cover and paperback

Given hard - cover: $P(\text{fiction}|\text{hard - cover}) = 0.45$ and $P(\text{non - fiction}|\text{hard - cover})=0.55$. Given paperback: $P(\text{fiction}|\text{paperback}) = 0.45$ and $P(\text{non - fiction}|\text{paperback})=0.55$. The probability of buying fiction versus non - fiction is the same regardless of whether the person buys a hard - cover or paperback.

Step3: Analyze overall probability of fiction and non - fiction

Overall, $P(\text{fiction})=0.35\times0.45 + 0.65\times0.45=(0.35 + 0.65)\times0.45=0.45$ and $P(\text{non - fiction})=0.35\times0.55+0.65\times0.55=(0.35 + 0.65)\times0.55 = 0.55$. So the probability of buying non - fiction is larger than buying fiction.

Answer:

C. The probability of buying fiction versus nonfiction is the same regardless of whether or not the person buys a hardcover or paperback.