Question

select the correct answer.

four books, one each on physics, chemistry, mathematics, and biology are about to be stacked on a shelf. if the books are stacked randomly, what is the probability the mathematics book is on top?

\\(\bigcirc\\ \frac{1}{2}\\)

\\(\bigcirc\\ \frac{1}{4}\\)

\\(\bigcirc\\ \frac{1}{6}\\)

\\(\bigcirc\\ \frac{1}{24}\\)

Explanation:

Calculate the total number of possible arrangements

$$ N_{\text{total}} = 4! = 24 $$

Calculate the number of favorable arrangements

$$ N_{\text{favorable}} = 1 \times 3! = 6 $$

Calculate the probability

$$ P(\text{Math on top}) = \frac{N_{\text{favorable}}}{N_{\text{total}}} = \frac{6}{24} = \frac{1}{4} $$

Answer:

• (A) \(\frac{1}{2}\)
• (B) \(\frac{1}{4}\) (Correct answer)
• (C) \(\frac{1}{6}\)
• (D) \(\frac{1}{24}\)