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Libniz

In probabilityland, one third of population is senior. Every winter 20% of population gets the flu. on average, two out of five seniors get the flu. what is the probability that a person with the flu is senior?

  • one year ago
  • one year ago

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  1. Libniz
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    here is what I did

    • one year ago
  2. Libniz
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    |dw:1348935331451:dw|

    • one year ago
  3. Libniz
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    "that's probability of senior with flu" whereas they are asking for "probability of person with a flu being a senior" I am not sure if they are same

    • one year ago
  4. Libniz
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    @zarkon

    • one year ago
  5. Libniz
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    or let event A be senior event B be people with flu A=1/3 S B=.2 S 2/5B=(A ∩ B) probability of people with flu being a senior (A ∩ B) ------------ B

    • one year ago
  6. Zarkon
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    so what is your answer

    • one year ago
  7. Libniz
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    well, I thought it was 2/15 but I am having second thoughts

    • one year ago
  8. Zarkon
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    you want P(senior|flu) correct?

    • one year ago
  9. Libniz
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    yes, probability of people with flu who are senior

    • one year ago
  10. Zarkon
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    \[P(S|F)=\frac{P(F|S)P(S)}{P(F)}\]

    • one year ago
  11. Libniz
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    so , P(F|S) is what I found to be 2/15?

    • one year ago
  12. Zarkon
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    \[P(F|S)=\frac{2}{5}\]

    • one year ago
  13. Libniz
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    ok, also is this a defination \[P(S|F)=\frac{P(F|S)P(S)}{P(F)}\]

    • one year ago
  14. Zarkon
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    \[P(A|B)=\frac{P(A\cap B)}{P(B)}\] is the definition of conditional probability

    • one year ago
  15. Zarkon
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    use this definition twice to get the formula I have above

    • one year ago
  16. Zarkon
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    \[P(A|B)=\frac{P(A\cap B)}{P(B)}\] \[P(B|A)=\frac{P(A\cap B)}{P(A)}\Rightarrow P(B|A)P(A)=P(A\cap B) \] then \[P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{P(B|A)P(A)}{P(B)}\]

    • one year ago
  17. Libniz
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    wow, thank you very much

    • one year ago
  18. Zarkon
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    np

    • one year ago
  19. Zarkon
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    do you have a new final answer?

    • one year ago
  20. Libniz
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    (2/5)(1/3) --------- = (1/5) 2/15 ----- = 1/5 2/15 * 5/1=2/3

    • one year ago
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