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Thread: Probability of being chosen

  1. #1
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    Question 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?
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  2. #2
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    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.
    . . $\displaystyle P(\text{3 seniors}) \:=\:\frac{56}{1140}$


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

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  3. #3
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    Thank you!

    What does the "v" mean though in the last part?
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  4. #4
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    Quote Originally Posted by kilgoretrout View Post
    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’?
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