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A hat contains slips of paper with the names of the 26 other students in Eduardo's class, 10 of whom are boys. To determine his partners for the group project, Eduardo has to pull two names out of the hat without replacing them.

What is the probability that both of Eduardo's partners for the group project will not be boys?

A. [tex]$\frac{9}{65}$[/tex]
B. [tex]$\frac{24}{65}$[/tex]
C. [tex]$\frac{64}{169}$[/tex]
D. [tex]$\frac{128}{325}$[/tex]



Answer :

GinnyAnswer
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].

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