# Probability of being chosen

• Nov 24th 2009, 01:59 PM
kilgoretrout
Probability of being chosen
Hi there, I need a bit of help on a probability question I was given for homework. I'm getting confused with keeping straight the different formulas. Can you help?

A casting for a play is being held at the local high school's gymnasium. There are a total of 20 actors of differing age groups that attended this casting call; they included 5 children, 7 adults, and 8 seniors. There are only 3 acting roles available for the play and the casting director decided to randomly fill these roles by drawing 3 of the 20 actors' name from a box. Assuming all 3 acting roles in the play are different, what is the probability that 3 actors of the same age range were chosen for the play?
• Nov 24th 2009, 02:36 PM
Soroban
Hello, kilgoretrout!

We don't need a lot of fancy formulas . . .

Quote:

A casting for a play is being held at the local high school's gymnasium.
There are a total of 20 actors of differing age groups that attended this casting call;
they included 5 children, 7 adults, and 8 seniors.

There are only 3 acting roles available for the play and the casting director
decided to fill these roles by randomly drawing 3 of the 20 actors' name from a box.

Assuming all 3 acting roles in the play are different, what is the probability
that 3 actors of the same age range were chosen for the play?

There are: . ${20\choose3} \:=\:1140$ possible choices.

3 children: . ${5\choose3} \:=\:10$ ways.
. . $P(\text{3 children}) \:=\:\frac{10}{1140}$

3 adults: . ${7\choose3} \:=\:35$ ways.
. . $P(\text{3 adults}) \:=\:\frac{35}{1140}$

3 seniors: . ${8\choose3} \:=\:56$ ways.
. . $P(\text{3 seniors}) \:=\:\frac{56}{1140}$

$P\bigg(\text{(3 children)} \vee \text{(3 adults)} \vee \text{(3 senors)}\bigg) \;=\;\frac{10}{1140} + \frac{35}{1140} + \frac{56}{1140} \;=\;\frac{101}{1140}$

• Nov 24th 2009, 04:03 PM
kilgoretrout
Thank you!

What does the "v" mean though in the last part?
• Nov 24th 2009, 04:38 PM
Plato
Quote:

Originally Posted by kilgoretrout
What does the "v" mean though in the last part?

You have been give a complete solution.
You could just turn that in for full credit.
But you don't even understant that $\vee$ means 'or'.
So how much help do you think that complete ready to hand-in solution really helps you?
If you are given a complete solution over against being asked to being asked to find a solution for yourself actually impairs your learning process.

Do you want to understand or do you want to ‘get over’?