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

Explanation:

Step1: Calculate number of non - boys

There are 26 students in total and 10 are boys. So the number of non - boys is $26 - 10=16$.

Step2: Calculate probability of first non - boy

The probability of pulling a non - boy on the first draw is $\frac{16}{26}$.

Step3: Calculate probability of second non - boy

Since we don't replace the first name, for the second draw, there are 15 non - boys left out of 25 students. So the probability of pulling a non - boy on the second draw is $\frac{15}{25}$.

Step4: Calculate combined probability

The probability that both are non - boys is the product of the probabilities of each draw. So $P=\frac{16}{26}\times\frac{15}{25}=\frac{16\times15}{26\times25}=\frac{240}{650}=\frac{24}{65}$.

Answer:

$\frac{24}{65}$