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anonymous one year ago Bobby is testing the effectiveness of a new cough medication. There are 100 people with a cough in the study. Seventy patients received the cough medication, and 30 other patients did not receive treatment. Thirty-four of the patients who received the medication reported no cough at the end of the study. Twenty of the patients who did not receive medication reported no cough at the end of the study. What is the probability that a patient chosen at random from this study took the medication, given that they reported no cough?

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1. anonymous

$P(\text{took medicine}|\text{no cough})=\frac{P(\text{took medicine AND no cough})}{P(\text{no cough})}$ Of the people that received the treatment, how many reported coughing afterward? Of the total 100 people in the study, how many reported coughing?

2. anonymous

46?

3. anonymous

right?

4. anonymous

46 reported coughing and 54 did

5. anonymous

didnt*

6. anonymous

Right, 54 people of the total 100 reported no coughing, so $$\dfrac{54}{100}=P(\text{no cough})$$. What about the other group?

7. anonymous

no cough would be whose left, right? so that's 46

8. anonymous

No, you already determined the number of no-coughs from the whole group. Now we're interested in the no-coughs from the group that got the treatment.

9. anonymous

oh 36

10. anonymous

Close, 36 is the number people that got treatment and DID report coughing.

11. anonymous

|dw:1442799451505:dw|

12. anonymous

so 46

13. anonymous

70+54=124

14. anonymous

i was a bit confused

15. anonymous

because the total people who didnt cough and the total who did take the meds would equal 124... right?

16. kropot72

|dw:1442799654988:dw| $\large p(med/no\ cough)=0.7\times\frac{34}{70}=0.34$ $\large P(no\ med/no\ cough)=0.3\times\frac{20}{30}=0.2$ $\large P(med|no\ cough)=\frac{0.34}{(0.34+0.2)}=0.63$

17. kropot72

@tekman1298 An alternative approach, using a probability tree.

18. anonymous

woah no way... i guessed right xD i decided to ask here for a double check

19. anonymous

thx, time for another?

20. kropot72

Was your guess 0.63?

21. anonymous

yes xD

22. kropot72

Cool. I have to log out now, please post as a new question.

23. anonymous

ok thx man

24. kropot72

You're welcome :)

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