
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 18th, 2018, 05:21 AM  #1 
Newbie Joined: Dec 2018 From: India Posts: 1 Thanks: 0  Calculating theoretical probability
Hello All, I have the following question in one of my tutorials. I need some help in resolving this. Background: A manufacturing company developed 40000 new drugs and they need to be tested. Question The QA checks on the previous batches of drugs found that — it is 4 times more likely that a drug is able to produce a better result than not. If we take a sample of 10 drugs, we need to find the theoretical probability that at most 3 drugs are not able to do a satisfactory job. a.) Propose the type of probability distribution that would accurately portray the above scenario, and list out the three conditions that this distribution follows. b.) Calculate the required probability. Thanks, Vicky Last edited by skipjack; December 18th, 2018 at 05:24 AM. 
December 18th, 2018, 10:32 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,264 Thanks: 1198 
The number of drugs out of the sample of 10 that produce a better result has a binomial distribution. $P[\text{a given drug produces a better result}] = \dfrac 4 5 = 0.8$ $P[\text{at most 3 drugs out of sample of 10 do not produce better result}] = \\ P[\text{at least 7 drugs out of sample do produce a better result} = \\ \sum \limits_{k=7}^{10}~\dbinom{10}{k}\left(\dfrac 4 5\right)^k \left(\dfrac 1 5\right)^{10k} = \dfrac{8585216}{9765625} \approx 0.88$ We could look at it another way where we define success as the drug not producing a better result. In that case we'd have $P[\text{at most 3 drugs don't produce better result}] = \\ \sum \limits_{k=0}^3~\dbinom{10}{k}\left(\dfrac 1 5\right)^k \left(\dfrac 4 5\right)^{10k} \\ \text{and this of course produces the same result}$ 

Tags 
calculating, cumulative distribution, probability, theoretical, theoretical probability 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Theoretical probability  brake4country  Probability and Statistics  3  July 14th, 2017 05:09 PM 
Theoretical Probability  Indigo28  Algebra  1  April 7th, 2017 10:30 PM 
theoretical question on probability theory  FemaleDiogenes  Advanced Statistics  9  March 24th, 2012 04:14 AM 
Calculating probability  kaspyanand  Algebra  2  July 6th, 2008 10:07 AM 
Empirical or Theoretical Probability?  symmetry  Advanced Statistics  2  January 29th, 2007 02:25 PM 