# Thread: Probability of being chosen

1. ## 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?

2. Hello, kilgoretrout!

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

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

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

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

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

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

3. Thank you!

What does the "v" mean though in the last part?

4. 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 $\displaystyle \vee$ 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?

#### Search Tags

chosen, probability 