To answer each question, we'll calculate the probabilities based on Ravi's selections without replacement.
Question 1: What is the probability of selecting a historical fiction book and then a romance novel?
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Probability of selecting a historical fiction book first:
- There are 12 historical fiction books out of 50 total books.
- Probability = \( \frac{12}{50} \)
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After selecting one historical fiction book, 49 books remain, and there are still 8 romance novels.
- Probability of selecting a romance novel second = \( \frac{8}{49} \)
The combined probability for both events (historical fiction first, then romance) is: \[ \frac{12}{50} \times \frac{8}{49} = \frac{12 \times 8}{50 \times 49} = \frac{96}{2450} \] The correct response is: \[ \frac{12}{50} \times \frac{8}{49} \]
Question 2: What is the probability that he picks a nonfiction book and then a mystery novel?
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Probability of selecting a nonfiction book first:
- There are 15 nonfiction books out of 50 total books.
- Probability = \( \frac{15}{50} \)
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After selecting one nonfiction book, 49 books remain, and there are still 15 mystery novels.
- Probability of selecting a mystery novel second = \( \frac{15}{49} \)
The combined probability for both events (nonfiction first, then mystery) is: \[ \frac{15}{50} \times \frac{15}{49} = \frac{15 \times 15}{50 \times 49} = \frac{225}{2450} \] The correct response is: \[ \frac{15}{50} \times \frac{15}{49} \]
Through the calculations, the correct answers to the questions are:
- \( \frac{12}{50} \times \frac{8}{49} \) for Question 1
- \( \frac{15}{50} \times \frac{15}{49} \) for Question 2