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:

Answer:

First, find the number of non - boys. There are \(26\) students in total and \(10\) are boys, so the number of non - boys is \(26 - 10=16\).

The probability of pulling a non - boy on the first draw is \(\frac{16}{26}\).
On the second draw (without replacement), the number of non - boys left is \(15\) and the total number of students left is \(25\), so the probability of pulling a non - boy on the second draw is \(\frac{15}{25}\).

The probability that both are non - boys is \(\frac{16}{26}\times\frac{15}{25}=\frac{240}{650}=\frac{24}{65}\)

So the answer is \(\frac{24}{65}\)