# Thread: conditional probability question that I am having trouble with

1. ## conditional probability question that I am having trouble with

There are 100 people with a certain disease. Of these, 10 are randomly selected to receive a drug that increases the number cured from 50 to 75 percent. what is the probability that a person received the drug if he is known to be cured?

2. ## Re: conditional probability question that I am having trouble with

C is the patient being cured & R is the occurance the patient has recieved the drug.

You need to find $\displaystyle P(R/C)= \frac{P(R\cap C)}{P(C)}$ where $\displaystyle P(C)= \frac{75}{100}, P(R)= \frac{10}{100}$

Now find $\displaystyle P(R\cap C)$ and you have everything you require.

3. ## Re: conditional probability question that I am having trouble with

Originally Posted by makaveli2178
There are 100 people with a certain disease. Of these, 10 are randomly selected to receive a drug that increases the number cured from 50 to 75 percent. what is the probability that a person received the drug if he is known to be cured?
$\mathcal{P}(D|C)=\frac{\mathcal{P}(D\cap C)}{\mathcal{P}(D\cap C)+\mathcal{P}(D^c\cap C)}$.