Answer :
To determine the probability that the mathematics book is on top when four books are stacked randomly on a shelf, we can proceed with the following steps:
1. Identify the Total Outcomes:
- There are a total of 4 books, and each book can be on the top position.
- Therefore, there are 4 possible outcomes for which book is on top (physics, chemistry, mathematics, or biology).
2. Identify the Favorable Outcomes:
- We are interested in the specific case where the mathematics book is on the top of the stack.
- There is only 1 favorable outcome for this scenario where the mathematics book is on top.
3. Calculate the Probability:
- The probability of an event is given by the formula:
[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
- In this case:
[tex]\[ \text{Probability} = \frac{1}{4} \][/tex]
Therefore, the probability that the mathematics book is on top is \(\frac{1}{4}\).
So, the correct answer is [tex]\( \boxed{\frac{1}{4}} \)[/tex].
1. Identify the Total Outcomes:
- There are a total of 4 books, and each book can be on the top position.
- Therefore, there are 4 possible outcomes for which book is on top (physics, chemistry, mathematics, or biology).
2. Identify the Favorable Outcomes:
- We are interested in the specific case where the mathematics book is on the top of the stack.
- There is only 1 favorable outcome for this scenario where the mathematics book is on top.
3. Calculate the Probability:
- The probability of an event is given by the formula:
[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
- In this case:
[tex]\[ \text{Probability} = \frac{1}{4} \][/tex]
Therefore, the probability that the mathematics book is on top is \(\frac{1}{4}\).
So, the correct answer is [tex]\( \boxed{\frac{1}{4}} \)[/tex].
