Question

A hat contains slips of paper with the names of the 26 other students in Eduardo’s 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 Eduardo’s partners for the group project will be girls?

Answer 1

So the probability that Eduardo pulls out a girl the first time is 16/26 (26 - 10 = 16) which means that pulling out a girl a second time would be 15/25. To find out the probability of both, you have to multiply the fractions together. So (16 × 15)/(25 × 26) which is 240/650. You can simplify this to 24/65, and I believe that is the furthest you can simplify it, which means that the answer is 24/65, I hope this helps!

Answer 2

Answer:

The probability that both of Eduardo’s partners for the group project will be girls is  $\frac{24}{65}$      

Step-by-step explanation:

Given : A hat contains slips of paper with the names of the 26 other students in Eduardo’s 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.

To find :  What is the probability that both of Eduardo’s partners for the group project will be girls?

Solution :

Total number of students = 26

Number of boys = 10

Number of girls = 26-10=16

Eduardo has to pull two names out of the hat without replacing them.

$\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}$

For the first hat,

Favorable outcome of getting girl = 16

Total number of outcome = 26

$\text{Probability}=\frac{16}{26}=\frac{8}{13}$

For the second hat, without replacement

Favorable outcome of getting another girl = 15

Total number of outcome = 25

$\text{Probability}=\frac{15}{25}=\frac{3}{5}$

The probability that both of Eduardo’s partners for the group project will be girls is

$\frac{8}{13}\times \frac{3}{5}=\frac{24}{65}$