+ Reply to Thread
Results 1 to 3 of 3

Thread: Need help with joint distribution problems

  1. #1
    Points: 55, Level: 1
    Level completed: 10%, Points required for next Level: 45

    Posts
    4
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Need help with joint distribution problems




    1. You need $30,000. Suppose that there is a 20% chance that Bank of
    America will loan you $30,000, a 30% chance that Wells Fargo will loan you $20,000, and a 40% chance that Washington Mutual will loan you $10,000. What is the probability that you will be able to borrow enough money?


    What I did: There's a 1 - (1-0.2)(1-0.3)(1-0.4) = 66% chance that at least one of those banks will lend you money. If $10k is enough, then that'll do. But I don't know how to find out the probability of being able to borrow enough money (30k)...

    2. A bundle of 40 t-shirts are delivered to the store. They randomly select 4 t-shirts for inspection. If none or one is defective, the bundle is accepted. If two or more are
    defective, the bundle is rejected. What is the probability that the bundle will be rejected if only 10% of the bundle is defective?


    What I did: So 4 t-shirts are defective, and 36 are not. The probability of getting a defective shirt is 4/40, and the probability of not getting an effective shirt is 36/40. The probability that the shirt is accepted is 37/40, and the probability that a shirt is rejected is 2/40?
    I am having such a hard time with these problems, can you guys show me a step-by-step process on how I can arrive to the answer?


    Thanks!

  2. #2
    TS Contributor
    Points: 22,410, Level: 93
    Level completed: 6%, Points required for next Level: 940

    Posts
    3,020
    Thanks
    12
    Thanked 565 Times in 537 Posts

    Re: Need help with joint distribution problems

    1. You have 30k if A loan Or F & W loan.

    2. Hypergeometric distribution.

  3. #3
    Points: 1,097, Level: 17
    Level completed: 97%, Points required for next Level: 3

    Location
    Philadellphia, PA
    Posts
    68
    Thanks
    1
    Thanked 20 Times in 18 Posts

    Re: Need help with joint distribution problems


    1. Step by step

    ... BOA WF WM
    Yes 0.2 0.3 0.4
    .No 0.8 0.7 0.6

    These are the 8 possible outcomes, the last column shows total money raised

    BOA WF WM
    Yes Yes Yes $60,000.00
    Yes Yes No $50,000.00
    Yes No Yes $40,000.00
    Yes No No $30,000.00
    No Yes Yes $30,000.00
    No Yes No $20,000.00
    No No Yes $10,000.00
    No No No $0.00

    So the first 5 cases raise $30,000 or more:

    (BOA Yes) and (WF Yes) and (WM Yes) = 0.2 * 0.3 * 0.4 = 0.024
    (BOA Yes) and (WF Yes) and (WM No ) = 0.2 * 0.3 * 0.6 = 0.036
    (BOA Yes) and (WF No ) and (WM Yes) = 0.2 * 0.7 * 0.4 = 0.056
    (BOA Yes) and (WF No ) and (WM No ) = 0.2 * 0.7 * 0.6 = 0.084
    (BOA No ) and (WF Yes) and (WM Yes) = 0.8 * 0.3 * 0.4 = 0.096

    Adding up those probabilities, you get 0.296

    Or what BGM said

    (BOA Yes) or (BOA No and WF Yes and WM Yes)
    =(0.2) or (0.8 and 0.3 and 0.4)
    =(0.2) + (0.8 * 0.3 * 0.4)
    =0.296
    Last edited by asterisk; 10-04-2013 at 12:24 PM.

+ 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