There are 6 forwards and 4 guards on the Tigers girls basketball team. Coach Briggs will randomly choose two captains for the next game. What is the probability that both captains will be forwards?

Respuesta :

[tex]\frac{1}{3}[/tex]

1) Let's find the sample space, i.e. the number of the total outcomes (favorable and not favorable). Let's consider that we need to pick 2 out of ten, that is our sample space.

[tex]_{10}C_2=\frac{10!}{2!\times8!}=45[/tex]

2) Now, let's find the number of favorable events. In this case, both players must be a forward. The favorable event includes only forward players out of those 6:

[tex]_6C_2=\frac{6!}{2!(6-2)!}=15[/tex]

3) We can write out the probability of picking one forward and another forward. Note that there was no replacement after each picking:

[tex]P=\frac{15}{45}=\frac{1}{3}[/tex]