Sure, let’s solve the problem step by step.
The question asks for the probability that the mathematics book is on top when four books (one each on physics, chemistry, mathematics, and biology) are stacked one on top of the other.
1. Identify the total number of possible outcomes:
There are four books, and any of these books can be placed on top, underneath which any of the remaining three books can be placed next, and so on. This creates a permutation problem. However, since we are only interested in the probability of the mathematics book being on top, the total number of possible outcomes for the top book is determined by the 4 books available.
2. Number of favorable outcomes:
There is only one favorable outcome where the mathematics book is on top out of the total 4 possible outcomes.
3. Calculate the probability using the formula:
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
4. Substitute the values:
[tex]\[
\text{Probability} = \frac{1}{4}
\][/tex]
Therefore, the probability that the mathematics book is on top is [tex]\(\frac{1}{4}\)[/tex].
So, the correct answer is:
B. [tex]\(\frac{1}{4}\)[/tex]
