My Math Forum Probability of drawing one company

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 January 9th, 2011, 10:17 AM #1 Newbie   Joined: Jan 2011 Posts: 5 Thanks: 0 Probability of drawing one company You have 214 companies in the database. What is the the probability of drawing 8 times one same company, among 6 companies you are drawing in each drawing, in 10 drawings.
 January 9th, 2011, 01:01 PM #2 Newbie   Joined: Jan 2011 Posts: 22 Thanks: 0 Re: Probability of drawing one company You need to clarify the question, the word 'drawing' appears 4 times there, I don't really understand what you're asking...
 January 9th, 2011, 02:05 PM #3 Newbie   Joined: Jan 2011 Posts: 5 Thanks: 0 Re: Probability of drawing one company What is the probability of drawing one same company among 6 drawn companies in 8 drawings out of 10. In each drawing you are drawing 6 companies out of the 214 companies. Is this more understandable now?
 January 9th, 2011, 10:53 PM #4 Newbie   Joined: Jan 2011 Posts: 5 Thanks: 0 Re: Probability of drawing one company 1 : 61 601 111 258 ?
 January 10th, 2011, 12:16 AM #5 Newbie   Joined: Jan 2011 Posts: 22 Thanks: 0 Re: Probability of drawing one company I still don't understand the problem, or what "1 : 61 601 111 258 ?" is for, but I'll tell you how to solve what I think the problem is. P(same company) = 1/214 * 6 = 6/214 (because you have 6 chances from each draw) P(¬same company) = 208/214 Using binomial distribution: $\frac{10!}{8!2!} * \frac{6}{214}^8*\frac{208}{214}^2= 45 * 3.819*10^{-13} * 0.945 = 1.624 * 10^{-11}$ Pretty unlikely, as you'd expect... Can anyone else confirm that?
 January 10th, 2011, 01:24 PM #6 Newbie   Joined: Jan 2011 Posts: 5 Thanks: 0 Re: Probability of drawing one company Agree with p=1/214*6 Expression for probability of independent repeated events is P=(n above k)*p^k*q^(n-k); where p=see row above, q=(1-p), k=8 and n=10
 January 10th, 2011, 01:33 PM #7 Newbie   Joined: Jan 2011 Posts: 5 Thanks: 0 Re: Probability of drawing one company Cimoo you are totaly right !!! 1/1.624*E-11= 61 576 354 680 (because you used just 3 decimal numbers)

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