A class of 8 maths students and 5 science students are ordered randomly. What
is the probability that the 6th position is occupied by a science student?

To find the probability that the 6th position is occupied by a science student, we need to consider the total number of students and the number of ways to assign a science student to the 6th position.

### Step-by-step solution:

1. **Total students**:  
   There are \(8\) math students and \(5\) science students, so the total number of students is:  
   \[
   8 + 5 = 13
   \]

2. **Favorable outcomes**:  
   We want the 6th position to be occupied by a science student. Since there are \(5\) science students, there are \(5\) favorable outcomes (i.e., we can choose any one of the 5 science students to fill this position).

3. **Total possible outcomes**:  
   Any one of the \(13\) students can be placed in the 6th position, so there are \(13\) possible outcomes.

4. **Probability**:  
   The probability is the ratio of favorable outcomes to total possible outcomes:
   \[
   P(\text{science student in 6th position}) = \frac{5}{13}
   \]

Thus, the probability that the 6th position is occupied by a science student is \( \frac{5}{13} \).

Would you like a more detailed breakdown or have any further questions?

### Related questions:
1. What is the probability that the first and last positions are both occupied by math students?
2. How would the probability change if there were only 4 science students?
3. What is the probability that a math student occupies the 3rd position?
4. What is the probability that the 6th position is occupied by either a math or a science student?
5. If the students are divided into two groups, one for math and one for science, how many different ways can the groups be arranged?

### Tip:
Always remember that probabilities range between 0 and 1, and the sum of all possible outcomes' probabilities equals 1!

A class of 8 maths students and 5 science students are ordered randomly. What is the probability that the 6th position is occupied by a science student?

Understand how to calculate the probability that a science student occupies the 6th position in a random ordering of 8 math and 5 science students. This problem covers key probability concepts and provides a step-by-step solution. Ideal for students in Grades 7-9.

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