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Probability qn

  1. Sep 27, 2015 #1
    1. The problem statement, all variables and given/known data

    Screen Shot 2015-09-27 at 10.46.14 PM.png

    Q1. In 10'000 typical young people, if 1% of non cannabis users develop psychosis, how many cannabis users would be expected to develop psychosis? Ans:28

    Q2. The report states:
    "About 20% of young people now report using cannabis"
    "... individuals who used cannabis were 41% more likely to have any psychosis"
    Given these two figures, and assuming that the incidence of pyschosis for reasons other than cannabis use is the same in both users and non users, what is the percentage of those with psychosis who have it due to cannabis use? (answer to nearest 1%). Ans: 8%

    3. The attempt at a solution

    1. P(cannabis ∩ psychosis) = P(cannabis) P(psychosis l cannabis) = 0.2 x 0.0141= 0.00282
    Number of young cannabis users with psychosis = 0.00282 x 10000 = 28.2

    2. P (cannabis l pyschosis) = P (cannabis ∩ psychosis) / P (psychosis)
    = P (psychosis l cannabis) P (cannabis) / P (psychosis ∩ (cannabis ∪ non-cannabis))
    = P (psychosis l cannabis) P (cannabis) / P [(psychosis ∩ cannabis) ∪ (psychosis ∩ non- cannabis)]
     
    Last edited: Sep 27, 2015
  2. jcsd
  3. Sep 27, 2015 #2

    mfb

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    Staff: Mentor

    How did you get that number? It's probably a rounding error.
     
  4. Sep 27, 2015 #3
    Which number are you referring to? If you are referring to the 8%, it was taken from the answer sheet. Otherwise, it is stated in the question.
     
  5. Sep 27, 2015 #4

    mfb

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    Staff: Mentor

    Edit: rounding error on my side, I used the number 28 instead of the more precise 28.2.

    Out of 10000, we have:
    8000 non-users, with 80 with psychosis and 7920 without
    2000 users, with 28.2 with psychosis and 1971.8 without
    Out of the 28.2, 20 have psychosis for other reasons (1% of 2000), 8.2 are attributed to cannabis consumption.

    => In total 108.2 with psychosis, 8.2 due to cannabis consumption. 8.2/108.2 = 0.0758, or 8% after rounding. Okay. With 8 instead of 8.2 I got 0.0741 which would give 7%.
     
  6. Sep 27, 2015 #5
    Thanks:) that is of great help!
     
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