# probability

• Jul 7th 2007, 05:08 PM
mkcar
probability
Hi, I just can not get how to find the probabillity of this question.
A doctor gives a patient a 60% chance of surviving bypass surgery after a heart attack. If the patient survives the surgery, he has a 50% chance that the heart damag will heall. Find the probbility that the patient survives surgery and the heart damage. No how do I do the math to solve this? thanks
• Jul 7th 2007, 05:53 PM
Jhevon
Quote:

Originally Posted by mkcar
Hi, I just can not get how to find the probabillity of this question.
A doctor gives a patient a 60% chance of surviving bypass surgery after a heart attack. If the patient survives the surgery, he has a 50% chance that the heart damag will heall. Find the probbility that the patient survives surgery and the heart damage. No how do I do the math to solve this? thanks

is that exactly how the question was phrased?

there is a subtlety in the question that i am not able to decipher, but that's ok, everyone knows i'm not that good with probability.

Let $\displaystyle A$ be the event that the patient survives the surgery
Let $\displaystyle B$ be the event the patient recovers from the heart damage

If what you want is the probability that the patient survives the surgery AND recovers from the heart damage, then that is given by:

$\displaystyle P(A andB) = P(A \cap B) = P(A) \cdot P(B) = \frac {6}{10} \cdot \frac {5}{10} = \frac {3}{10}$

If what you want is the probability that a patient will recover from the heart damage, GIVEN they survived the surgery, then that is given by:

$\displaystyle P(BgivenA) = P(B | A) = \frac {P(A \cap B)}{P(A)} = \frac {P(A) \cdot P(B)}{P(A)} = P(B) = \frac {5}{10}$

based on how you phrased the question, I'd say you want the first answer, but something in the back of my mind is saying you want the second answer. I don't know which voice to listen to!

EDIT: I have decided to go with rualin's voice, he seems to know his stuff judging from his past posts. So go with the first answer, and better yet, use his notation
• Jul 7th 2007, 05:59 PM
rualin
I think he means the probability that a person who has had surgery will recover so P(A and B)=P(A)*P(B|A)=3/10 like you said
• Jul 8th 2007, 10:52 AM
mkcar
thank you!
Hi, yes I did need the answer to both, thank you
• Jul 8th 2007, 10:58 AM
rualin
I'm flattered but I'm really no expert. I just took an elementary statistics course last semester and remember what I did and what I had trouble with.

Don't be modest. You have much more "voice" than I do juding from your past nearly 3,000 posts.

But thanks. :D