18) A bookcase contains 6 math books and 12 accounting books. If a student randomly selects two books, then find the probability that both of them are math books or accounting books \begin{tabular}{ll} a) 0.0423 & b) 0.5556 \\ \hline c) 0.5000 & d) 0.5224 \\ \hline\end{tabular}

To determine the probability that both books selected are either math books or accounting books, we can follow these steps: 1. **Total Number of Books:** - Math books: 6 - Accounting books: 12 - **Total books = 6 + 12 = 18** 2. **Total Ways to Select 2 Books:** - Using combinations: \( \binom{18}{2} = \frac{18 \times 17}{2} = 153 \) 3. **Favorable Outcomes:** - **Both are Math Books:** - \( \binom{6}{2} = \frac{6 \times 5}{2} = 15 \) - **Both are Accounting Books:** - \( \binom{12}{2} = \frac{12 \times 11}{2} = 66 \) - **Total Favorable Outcomes = 15 + 66 = 81** 4. **Probability Calculation:** - \( \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{81}{153} \approx 0.5294 \) 5. **Selecting the Closest Answer:** - The closest option to 0.5294 is **d) 0.5224**. **Answer:** d) 0.5224