

Subject:
Probability
Category: Science > Math Asked by: vaacga List Price: $10.00 
Posted:
28 Jun 2006 16:58 PDT
Expires: 28 Jul 2006 16:58 PDT Question ID: 741879 
If an event has a probability of, say, 70% of occurring and 30% of not occurring, how can the probabilities be calculated that this event will occur none, once, twice, 3 times or all 4 times when attempted, say, 4 or n times? 

Subject:
Re: Probability
Answered By: liviofloresga on 28 Jun 2006 20:47 PDT Rated: 
Hi!! This is a typical problem of Binomial Distribution, see for references the following pages: "The Binomial Distribution": http://www.stat.tamu.edu/stat30x/notes/node66.html "Binomial distribution (1 of 3)": http://davidmlane.com/hyperstat/A2301.html Acording to the above pages the formula for the case where the number of trials is n=4 we have: P(X=0) = (4!/0!4!) * (0.7)^0 * (0.3)^4 = = 1 * 1 * 0.0081 = = 0.0081 (or 0.81%) P(X=1) = (4!/1!3!) * (0.7)^1 * (0.3)^3 = = 4 * 0.7 * 0.027 = = 0.0756 (or 7.56%) P(X=2) = (4!/2!2!) * (0.7)^2 * (0.3)^2 = = 6 * 0.49 * 0.09 = = 0.2646 (or 26.46%) P(X=3) = (4!/3!1!) * (0.7)^3 * (0.3)^1 = = 4 * 0.343 * 0.3 = = 0.4116 (or 41.16%) P(X=4) = (4!/4!0!) * (0.7)^4 * (0.3)^0 = = 1 * 0.2401 * 1 = = 0.2401 (or 24.01%) For n trials and x succeses just apply the formula: P(X=x) = (n!/x!(nx)!) * (0.7)^x * (0.3)^(nx) For more visit the following page, which has a Java applet where you can confirm the results and links to more examples: "The Binomial Distribution": http://www.stat.wvu.edu/SRS/Modules/Binomial/binomial.html Search strategy: My own knowledge to find the topic and the keyword "binomial distribution" at Google.com I hope this helps you. If you find something unclear please do not hesitate to request for a clarification, I will be glad to give you further assistance on this question if you need it. Regards, liviofloresga  
 

vaacga
rated this answer:
Very good and to the point answer.Hope I will not have any problems with it in the future 

There are no comments at this time. 
If you feel that you have found inappropriate content, please let us know by emailing us at answerssupport@google.com with the question ID listed above. Thank you. 
Search Google Answers for 
Google Home  Answers FAQ  Terms of Service  Privacy Policy 