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Game show there are 10 contestants of which 6 are female.

  1. Nov 24, 2011 #1
    1. The problem statement, all variables and given/known data
    At the start of a gameshow there are 10 contestants of which 6 are female. In each round of
    the game, one contestant is eliminated. All of the contestants have the same chance of
    progressing to the next round each time.

    Given that the first contestant to be eliminated is male, find the probability that the next
    two contestants to be eliminated are both female.


    2. Relevant equations
    p(next to be female|male)=(next to be female n male)/(male)

    3. The attempt at a solution
    I did (4/10)*(6/9)*(5/8)
    But when I checked the answer, it was (6/9)*(5/8).
    Why?
     
  2. jcsd
  3. Nov 24, 2011 #2

    Dick

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    Re: probability

    This is probably just a language issue. The problem says "Given that the first contestant to be eliminated is male". "Given" means that you assume the male is eliminated before you start calculating probabilities. It's called a conditional probability.
     
  4. Nov 24, 2011 #3
    Re: probability

    Ya, that's what I did. But how come I didn't get the same answer?
     
  5. Nov 24, 2011 #4
    Re: probability

    Or is there something wrong with my equation?
     
  6. Nov 24, 2011 #5

    Dick

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    Re: probability

    "Given" means something has already taken place and you don't factor in that probability. There's nothing wrong with the equation, but "given" means skip the 4/10 factor.
     
  7. Nov 24, 2011 #6

    HallsofIvy

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    Re: probability

    Originally, there were 10 contestants and 6 were female. Given that the first to be eliminated was male, there are now 9 contestants and 6 are female. What is the probability that the one eliminated now will be female? If that happens then there will be 8 contestants, 5 of them female. What is the probability that the one eliminated now will be female?
     
  8. Nov 24, 2011 #7
    Re: probability

    But how can I use the equation :

    P(A|B)=P(AnB)/P(B)

    to get the answer?Or is it not possible, because the total number of people decreases?
     
  9. Nov 24, 2011 #8

    Ray Vickson

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    Re: probability

    Sometimes we use that equation in reverse. When we know P(B) and P(A|B) we can use the equation to get P(AnB). That is what is happening in this problem.

    RGV
     
  10. Nov 24, 2011 #9
    Re: probability

    so what's the value of P(AnB)?
     
  11. Nov 25, 2011 #10

    Ray Vickson

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    Re: probability

    Tell me what are A and B. You brought up the AnB, and I just responded to your question.

    RGV
     
  12. Nov 25, 2011 #11
    Re: probability

    (4/10)*(6/9)*(5/8)
    But it's not correct.
     
  13. Nov 25, 2011 #12

    Ray Vickson

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    Re: probability

    Of course not. As has already been explained clearly to you, there should be no 4/10 factor.

    RGV
     
  14. Nov 25, 2011 #13
    Re: probability

    the probability of two independent events A and B: P(AnB) is the probability of A times the probability of B. Thats two things, not three things. So, not (4/10)*(6/9)*(5/8). Just (6/9)*(5/8)
     
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