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 p

Question

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

Answer 1

Probability is defined as the "number of

favorable outcomes divided by the total

number of outcomes possible."  We can

write the probability of an event happening 

as a fraction in equation form...

 

P(Event)=(#favorable outcomes)/(total #outcomes) 

 

From the problem statement...

26...............total number of students

10...............number of boys

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

2.................number of partners Eduardo needs 

                    making two picks

 

So...P₁(girl)=(#girls)/(total student)

                    =16/26

   ∴ P₁(girl)=8/13......1st pick

 

Two names will be picked from the hat, so on the

second pick there will be 26-1=25 names to pick
from.  If a girl is first picked, then only 16-1=15

girls are left.  This is called a "dependent event"

as we are NOT replacing each picked name back

to the hat.  The second pick IS dependent on the

outcome of the first.

 

So...P₂(girl)=(#girls-1)/(total student-1)
                    =(16-1)/(26-1)

                    =15/25
   ∴ P₂(girl)=3/5......2nd pick

 

Now multiply the 1st and 2nd probability fractions...

 

   P(girl,girl)=P₁(girl) x P₂(girl)
                    =(8/13) x (3/5)

∴ P(girl,girl)=24/65...on 2 consecutive picks

  

There is a 24/65 chance that the first two picks 

will be girls.