To solve the problem of finding the probability that both of Eduardo's partners for the group project will not be boys, let's work through the following steps:
1. Determine the Total Number of Students:
- There are 26 students in total.
2. Find Out the Number of Boys and Girls:
- There are 10 boys.
- Therefore, the number of girls (not boys) is [tex]\(26 - 10 = 16\)[/tex].
3. Calculate the Probability of Picking a Girl on the First Draw:
- The total number of students is 26.
- The number of girls is 16.
- The probability that he picks a girl first is [tex]\(\frac{16}{26} = \frac{8}{13}\)[/tex].
4. Calculate the Probability of Picking a Girl on the Second Draw Given that the First was a Girl:
- After picking one girl, there are 25 students left (26 - 1).
- The number of girls left is 15 (16 - 1).
- The probability that he picks a girl on the second draw is [tex]\(\frac{15}{25} = \frac{3}{5}\)[/tex].
5. Calculate the Combined Probability:
- Multiply the two probabilities together to find the combined probability that both partners are girls:
[tex]\[
\frac{8}{13} \times \frac{3}{5} = \frac{24}{65}
\][/tex]
So, the probability that both of Eduardo's partners for the group project will not be boys is [tex]\(\boxed{\frac{24}{65}}\)[/tex].
