+ Reply to Thread
Results 1 to 3 of 3

Thread: "either but not both" ??

  1. #1
    Points: 6, Level: 1
    Level completed: 11%, Points required for next Level: 44

    Posts
    2
    Thanks
    0
    Thanked 0 Times in 0 Posts

    "either but not both" ??




    Hi,
    I was trying to complete this question, but I'm confused about where either but not both comes in:

    "certain chickens on a large farm have developed diseases, 2% have fatty liver syndrome, 3% have cage layer fatigue. 4% of the chickens have either one of these conditions, but not both"
    a) Find the percentage of poultry with both conditions
    b) a chicken is selected at random from this farm, what is the probability it has neither condition?

    Calling 'fatty liver syndrome' event A, and 'cage layer fatigue' event B
    What I have understood so far is that:
    P(A)=0.02
    P(B)=0.03

    P(A) + P(B) = 0.04

    Where this fits in a Venn diagram, I'm not too sure- since they are not mutually exclusive, there is P(AnB), but using the addition rule requires P(AuB), the conditions of which mean that A and B occur together, which is not equal to 0.04?

    thanks!

  2. #2
    Devorador de queso
    Points: 95,940, 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: "either but not both" ??

    Quote Originally Posted by rlm View Post
    Hi,

    What I have understood so far is that:
    P(A)=0.02
    P(B)=0.03
    These look fine

    P(A) + P(B) = 0.04
    This is wrong. Clearly this can't be true in light of what what we have at the top (which adds up to .05). The condition related to .04 is "have either one of the conditions - but not both" which means the chicken could have A but they don't have B, OR they could have B but they don't have A.
    I don't have emotions and sometimes that makes me very sad.

  3. #3
    Points: 6, Level: 1
    Level completed: 11%, Points required for next Level: 44

    Posts
    2
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: "either but not both" ??


    Thanks!
    So if A' is the complement of A and B' is the complement of B,
    then the 0.04 is equal to P(AnB')+ P(BnA'),
    So can that, as well as P(A) which includes all A, and P(B) which is all B, be used to find the P(AnB)?

    P(AnB) = P(A) + P(B) - [P(AnB')+ P(BnA')]

    on a Venn diagram, how would this work? P(A) would be the whole circle, and P(B) would be another whole circle interlapping with A and together the P(A) + P(B) would include P(AnB)?

    thanks!

+ 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