a hat contains slips of paper with the names of the 26 other students in eduardos class on them, 10 of whom…

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? $\frac{9}{65}$ $\frac{24}{65}$ $\frac{64}{169}$ $\frac{128}{325}$

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? $\frac{9}{65}$ $\frac{24}{65}$ $\frac{64}{169}$ $\frac{128}{325}$

Answer

Explanation:

Step1: Calculate number of girls

There are 26 students in total and 10 are boys, so the number of girls is $26 - 10=16$.

Step2: Calculate probability of first - pick being a girl

The probability of picking a girl on the first draw is $\frac{16}{26}=\frac{8}{13}$ since there are 16 girls out of 26 students.

Step3: Calculate probability of second - pick being a girl

After one girl is picked on the first draw, there are 15 girls left out of 25 students. So the probability of picking a girl on the second draw is $\frac{15}{25}=\frac{3}{5}$.

Step4: Calculate the probability of both events

Since the two draws are dependent events, the probability that both of Eduardo's partners are girls is the product of the probabilities of each draw. So $P=\frac{8}{13}\times\frac{3}{5}=\frac{24}{65}$.

Answer:

$\frac{24}{65}$