There are 50 books on a shelf. They include 15 mystery novels, 12 works of historical fiction, 8 romance novels, and 15 nonfiction books. Ravi must choose 2 books and doesn't really care which kind they are. He decides to randomly pick 1 and then pick another without replacement. If Federica randomly selects 2 books from the shelf, what is the probability of selecting a nonfiction book, and then a mystery novel.

Question

15/49
15/50*15/49
15/50
15/50*15/50

Answer 1

To find the probability of Ravi selecting a nonfiction book first and then a mystery novel without replacement, we can calculate it step by step.

1. Probability of selecting a nonfiction book first: There are 15 nonfiction books out of a total of 50 books. \[ P(\text{Nonfiction first}) = \frac{15}{50} \]

2. Probability of selecting a mystery novel second (after selecting a nonfiction book): After selecting the nonfiction book, there will be 49 books left (50 - 1 = 49), and all 15 mystery novels are still available. \[ P(\text{Mystery second | Nonfiction first}) = \frac{15}{49} \]

3. Total probability of both events happening: We multiply the probability of the first event by the probability of the second event following it: \[ P(\text{Nonfiction first and then Mystery}) = P(\text{Nonfiction first}) \times P(\text{Mystery second | Nonfiction first}) = \frac{15}{50} \times \frac{15}{49} \]

Putting it all together: \[ P(\text{Nonfiction first and then Mystery}) = \frac{15}{50} \times \frac{15}{49} = \frac{15 \times 15}{50 \times 49} = \frac{225}{2450} \] After reducing \( \frac{225}{2450} \) to its simplest form, we can divide both numerator and denominator by 25: \[ = \frac{9}{98} \]

However, the original set of options you provided seems to be focused on the combined probability calculation rather than its reduction. Thus, the correct choice from your provided options for the direct multiplication would simply be:

\[ \frac{15}{50} \times \frac{15}{49} \]

So, the answer is: \(\frac{15}{50} \times \frac{15}{49}\).