Question

a hat contains slips of paper with the names of the 26 other students in eduardos class on them, 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 eduardos partners for the group project will not be boys? \\(\frac{8}{65}\\) \\(\frac{24}{65}\\) \\(\frac{64}{169}\\) \\(\frac{128}{325}\\)

Explanation:

Step1: Find number of non - boys

Total other students = 26, number of boys = 10. So number of non - boys = 26 - 10 = 16.

Step2: Probability of first non - boy

Probability of pulling a non - boy first is $\frac{16}{26}=\frac{8}{13}$ (since there are 16 non - boys out of 26 students).

Step3: Probability of second non - boy (without replacement)

After pulling one non - boy, there are 15 non - boys left and 25 students left. So probability of pulling a non - boy second is $\frac{15}{25}=\frac{3}{5}$.

Step4: Multiply the probabilities

Since these are dependent events, we multiply the two probabilities: $\frac{8}{13}\times\frac{3}{5}=\frac{24}{65}$.

Answer:

$\frac{24}{65}$ (the option with $\frac{24}{65}$)