To determine the probability of being assigned a seat in the back row, follow these steps:
1. Calculate the total number of seats in the classroom:
- The front row has 8 seats.
- The middle row has 10 seats.
- The back row has 12 seats.
Adding these together, we get:
[tex]\[
\text{Total seats} = 8 + 10 + 12 = 30
\][/tex]
2. Determine the number of seats in the back row:
- The back row has 12 seats.
3. Calculate the probability of being assigned a seat in the back row:
- The probability is the ratio of the number of seats in the back row to the total number of seats.
[tex]\[
\text{Probability} = \frac{\text{Number of seats in the back row}}{\text{Total number of seats}} = \frac{12}{30}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{12}{30} = \frac{2}{5}
\][/tex]
So, the probability of being assigned a seat in the back row is:
[tex]\[
\frac{2}{5}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{2}{5}}
\][/tex]
