+ Reply to Thread
Results 1 to 11 of 11

Thread: Homework exercise

  1. #1
    Points: 21, Level: 1
    Level completed: 41%, Points required for next Level: 29

    Posts
    6
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Homework exercise




    I have a homework which can not be fully resolved with my knowlage:

    Firm has 10 employees, 2 womens and 8 mens. The Management Board will randomly select 3 employees and reward them with a trip to Venice. What is probability for:

    a.) the winners will be only womans
    b.) the winners will be only mans
    c.) the winners will be exactly 1 women (so other 2 are mans right?)
    d.) the winners will be exactly 2 womens (other 1 is man right?)
    e). among the winners will be at least 1 woman

    solved :

    a.) P(A) = 0 (only 2 womans employed)
    b.) P(A) = (8 3) / (10 3) = 7/15
    c.) P(A) = ((8 2) * (2 1)) / (10 3) -> wrong result
    d.) have no idea (all I tried was wrong)
    e.) have no idea (all I tried was wrong)

    Thanks for help.

  2. #2
    Points: 21, Level: 1
    Level completed: 41%, Points required for next Level: 29

    Posts
    6
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Re: Homework exercise

    I also tried to calculate c.) like this, but get wrong result :

    (3 2) * (8/10)^2 * (1-8/10)^1 = 0.384 -> wrong

  3. #3
    Devorador de queso
    Points: 95,889, Level: 100
    Level completed: 0%, Points required for next Level: 0
    Awards:
    Posting AwardCommunity AwardDiscussion EnderFrequent Poster
    Dason's Avatar
    Location
    Tampa, FL
    Posts
    12,937
    Thanks
    307
    Thanked 2,630 Times in 2,246 Posts

    Re: Homework exercise

    You answer for c looks fine to me. How do you know it's wrong?
    I don't have emotions and sometimes that makes me very sad.

  4. #4
    Points: 21, Level: 1
    Level completed: 41%, Points required for next Level: 29

    Posts
    6
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Re: Homework exercise

    Our teacher gave us results:

    a.) 0
    b.) 7/15
    c.) 7/15 = 0.467
    e.) 8/15 = 0.533

    d is made up by me, so I don't have a result.

  5. #5
    Devorador de queso
    Points: 95,889, Level: 100
    Level completed: 0%, Points required for next Level: 0
    Awards:
    Posting AwardCommunity AwardDiscussion EnderFrequent Poster
    Dason's Avatar
    Location
    Tampa, FL
    Posts
    12,937
    Thanks
    307
    Thanked 2,630 Times in 2,246 Posts

    Re: Homework exercise

    Quote Originally Posted by epicVoid View Post
    Our teacher gave us results:

    c.) 7/15 = 0.467
    Well why don't you retry computing what you have in your original post because that's what you end up getting.
    I don't have emotions and sometimes that makes me very sad.

  6. #6
    Points: 21, Level: 1
    Level completed: 41%, Points required for next Level: 29

    Posts
    6
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Re: Homework exercise

    I calculated all again and get this :

    a.) 0 // teacher's result = 0
    b.) (3 3) * (8/10)^3 * (1-8/10)^0 = 1 * 512/1000 * 1 = 0.512 // teacher's result = 7/15 = 0.467
    c.) (3 2) * (8/10)^2 * (1-8/10)^1 = 3 * 64/100 * 2/10 = 0.384 // teacher's result = 7/15 = 0.467
    d.) (3 1) * (8/10)^1 * (1-8/10)^2 = 3 * 8/10 * 4/100 = 0.096 // unknown result
    e.) c.) + d.) = 0.384 + 0.096 = 0.480 // teacher's result = 8/15 = 0.533


    All worng except a.)...

  7. #7
    Points: 4,841, Level: 44
    Level completed: 46%, Points required for next Level: 109
    Con-Tester's Avatar
    Posts
    167
    Thanks
    3
    Thanked 59 Times in 57 Posts

    Re: Homework exercise

    Problem c.) There are three possible ways to end up with exactly 1 woman in three selections: (M and M and W) or (M and W and M) or (W and M and M). The associated probabilities are P(M&M&W) = (8/10)(7/9)(2/8) = 14/90, P(M&W&M) = (8/10)(2/9)(7/8) = 14/90 and P(W&M&M) = (2/10)(8/9)(7/8) = 14/90. Any of these three outcomes will get the desired end result, and so the probability of ending up with exactly 1 woman is P(1W) = (14/90)+ (14/90)+ (14/90) = 42/90 = 7/15.

    Problem d.) There are three possible ways to end up with exactly 2 women in three selections: (M and W and W) or (W and M and W) or (W and W and M). The associated probabilities are P(M&W&W) = (8/10)(2/9)(1/8) = 1/45, P(W&M&W) = (2/10)(8/9)(1/8) = 1/45 and P(W&W&M) = (2/10)(1/9)(8/8) = 1/45. Any of these three outcomes will get the desired end result, and so the probability of ending up with 2 women is P(2W) = (1/45)+ (1/45)+ (1/45) = 3/45 = 1/15.

    Problem e.) There are two ways to end up with at least one woman: 1W or 2W. The associated probabilities are P(1W) = 7/15 and P(2W) = 1/15. Any of these two outcomes will get the desired end result, and so the probability of ending up with at least 1 woman is P(≥1W) = 7/15+1/15 = 8/15.

    The above methods show the value of understanding probability problems in terms of first principles (pigeonholing & counting), as well as the mathematical meaning of “and” and “or” when calculating the probabilities.

  8. The Following User Says Thank You to Con-Tester For This Useful Post:

    epicVoid (05-23-2014)

  9. #8
    Points: 21, Level: 1
    Level completed: 41%, Points required for next Level: 29

    Posts
    6
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Re: Homework exercise

    Thank you. I understand now.

  10. #9
    Devorador de queso
    Points: 95,889, Level: 100
    Level completed: 0%, Points required for next Level: 0
    Awards:
    Posting AwardCommunity AwardDiscussion EnderFrequent Poster
    Dason's Avatar
    Location
    Tampa, FL
    Posts
    12,937
    Thanks
    307
    Thanked 2,630 Times in 2,246 Posts

    Re: Homework exercise

    Quote Originally Posted by Con-Tester View Post
    Problem c.) There are three possible ways to end up with exactly 1 woman in three selections: (M and M and W) or (M and W and M) or (W and M and M). The associated probabilities are P(M&M&W) = (8/10)(7/9)(2/8) = 14/90, P(M&W&M) = (8/10)(2/9)(7/8) = 14/90 and P(W&M&M) = (2/10)(8/9)(7/8) = 14/90. Any of these three outcomes will get the desired end result, and so the probability of ending up with exactly 1 woman is P(1W) = (14/90)+ (14/90)+ (14/90) = 42/90 = 7/15.
    Once again though - their method in the initial post was fine. I don't understand why they think it was wrong. They gave: ((8 2) * (2 1)) / (10 3) - assuming that (8 2) means "8 choose 2" this gives us the desired result and is probably the easiest approach.
    I don't have emotions and sometimes that makes me very sad.

  11. #10
    Points: 21, Level: 1
    Level completed: 41%, Points required for next Level: 29

    Posts
    6
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Re: Homework exercise

    If I calculate ((8 2) * (2 1)) / (10 3), I get :

    (28 * 2) / 4320 = 0.00129...

  12. #11
    Points: 4,841, Level: 44
    Level completed: 46%, Points required for next Level: 109
    Con-Tester's Avatar
    Posts
    167
    Thanks
    3
    Thanked 59 Times in 57 Posts

    Re: Homework exercise


    Quote Originally Posted by epicVoid View Post
    If I calculate ((8 2) * (2 1)) / (10 3), I get :

    (28 * 2) / 4320 = 0.00129...
    Uhm, (10 3) = 120, not 4320.

+ Reply to Thread

           




Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats