To determine the probability that both of Eduardo's partners for the group project will not be boys, we can follow these steps:
1. Calculate the Total Students and Splitting of Students:
Eduardo's class has 26 students in total.
Out of those, 10 students are boys.
Therefore, 26 - 10 = 16 students are not boys (girls).
2. First Draw (First Partner):
The probability that the first student chosen is not a boy is the number of girls divided by the total number of students.
[tex]\[
\text{Probability (First partner not a boy)} = \frac{\text{Number of girls}}{\text{Total students}} = \frac{16}{26} = \frac{8}{13}
\][/tex]
3. Second Draw (Second Partner), Given the First Partner is Not a Boy:
If the first chosen student was not a boy, there will be one less girl and one less student in the total count.
Now, there are 15 girls and 25 students left.
The probability that the second student chosen is not a boy given the first was not a boy is:
[tex]\[
\text{Probability (Second partner not a boy | First partner not a boy)} = \frac{\text{Remaining number of girls}}{\text{Remaining total students}} = \frac{15}{25} = \frac{3}{5}
\][/tex]
4. Combined Probability:
The combined probability that both students chosen are not boys is the product of the probabilities of each step.
[tex]\[
\text{Combined Probability} = \left(\frac{8}{13}\right) \times \left(\frac{3}{5}\right) = \frac{24}{65}
\][/tex]
Therefore, the probability that both of Eduardo's partners for the group project will not be boys is:
[tex]\[
\boxed{\frac{24}{65}}
\][/tex]
