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?

Question

anonymous · Answer

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

anonymous · Answer

46?

anonymous · Answer

right?

anonymous · Answer

46 reported coughing and 54 did

anonymous · Answer

didnt*

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

oh 36

anonymous · Answer

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

anonymous · Answer

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