
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 8th, 2018, 11:32 PM  #1 
Newbie Joined: Feb 2018 From: Winnipeg Posts: 6 Thanks: 0  Probability problem
A doctor is using an adaptive response technique in their clinical trial to decide whether patients get drug A or a placebo. They start with one red ball and one green ball in a bucket. For patient one, they will pull out a ball and look at the colour. If it's a red ball, the patient gets drug A. If it's a green ball, the patient gets the placebo. If the patient receives a placebo, the doctor will do nothing to the bucket before selecting for the next patient. If the patient receives drug A and has a positive outcome, they will add a red ball to the bucket. If the patient receives drug A and have a negative outcome, they will add a green ball to the bucket. The second patient will have their treatment decided based on what is in now in the bucket and we will add balls or not according to the same rule. This continues for patient 3, etc... Suppose there is a constant probability of 0.60 that any patient who receives drug A will have a positive outcome. What is the probability patient 1 gets Drug A with a positive treatment, patient 2 gets a placebo, and patient 3 gets Drug A? I don't understand the question well enough. Can someone help me with a direction? Does the question wants me to find the probability of patient 3 gets drug A and patient 2 gets a placebo and patient 1 has a positive outcome given taking drug A? Thank you. Last edited by Shanonhaliwell; February 8th, 2018 at 11:39 PM. 
February 8th, 2018, 11:51 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,758 Thanks: 900 
this is just an exercise in chasing down a path in a probability tree. $P[p_1\text{ gets drug A with + results.}] = \left(\dfrac 1 2\right)\left(\dfrac 3 5\right) = \dfrac {3}{10}$ Now we add a red ball to the bucket due to the success so that there are now 2 red balls and 1 green ball. $P[p_2 \text{ gets a placebo.}] = \dfrac 1 3$ We do nothing due to $p_2$ receiving a placebo so $P[p_3 \text{ gets drug A.}] = \dfrac 2 3$ We multiply all these probabilities together to get the probability of the chain so $P[p_1 =A^+,~p_2 = P,~p_3=A] = \dfrac{3}{10}\dfrac{1}{3}\dfrac{2}{3} = \dfrac{6}{90} = \dfrac{1}{15}$ 

Tags 
probability, problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Probability Problem / Insurance problem  bsjmath  Advanced Statistics  2  March 1st, 2014 03:50 PM 
probability problem (2)  helloprajna  Probability and Statistics  9  November 9th, 2012 02:22 AM 
Probability Problem  joshuakosasih  Probability and Statistics  2  October 15th, 2012 02:31 AM 
Probability Problem.Please help  adiptadatta  Probability and Statistics  1  May 11th, 2010 07:46 AM 
a probability problem  duz  Real Analysis  4  December 31st, 1969 04:00 PM 