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 number of girls is $26 - 10=16$.

Step2: Calculate probability of first - pick being a girl

The probability that the first name drawn is a girl 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 (without replacement)

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

Step4: Calculate the probability of both events

The probability that both names drawn are girls (using the multiplication rule for independent - like events without replacement) is $\frac{8}{13}\times\frac{3}{5}=\frac{24}{65}$.

Answer:

$\frac{24}{65}$