To find the probability that both people chosen are females, let's solve the problem step by step:
1. Determine the total number of students:
- There are 5 female students and 5 male students.
- Total number of students = [tex]\( 5 + 5 = 10 \)[/tex].
2. Calculate the total number of ways to choose 2 students out of 10:
- We use the combination formula [tex]\( \binom{n}{r} \)[/tex] which represents the number of ways to choose [tex]\( r \)[/tex] items from [tex]\( n \)[/tex] items without regard to the order.
- Here, [tex]\( n = 10 \)[/tex] and [tex]\( r = 2 \)[/tex].
- [tex]\[ \binom{10}{2} = \frac{10!}{2!(10-2)!} = \frac{10 \times 9}{2 \times 1} = 45 \][/tex]
3. Calculate the total number of ways to choose 2 female students out of 5:
- Here, [tex]\( n = 5 \)[/tex] and [tex]\( r = 2 \)[/tex].
- [tex]\[ \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10 \][/tex]
4. Calculate the probability:
- The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
- The number of favorable outcomes is the number of ways to choose 2 females from 5, which we calculated as 10.
- The total number of possible outcomes is the number of ways to choose 2 students from 10, which we calculated as 45.
- [tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{10}{45} = \frac{2}{9} \][/tex]
Therefore, the probability that both people chosen are females is [tex]\( \frac{2}{9} \)[/tex].
So, the correct answer is:
[tex]\[ \frac{2}{9} \][/tex]
