hypergeom_solns

# hypergeom_solns - sketch of solutions for hypergeometric...

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sketch of solutions for hypergeometric distribution practice problems try to do these by reasoning from first principles, using combinations for selecting at random without replacement and the multiplication rule m 1 ways to select items/individuals of one type m 2 ways to select items/individuals of the other type then there are m 1 * m 2 total ways to select from Statistics, James T. McClave and Terry Sincich, Prentice-Hall 4.76 "Hotspots" are species-rich geographical areas. A Nature (Sept. 1993) study estimated the probability of a bird species in Great Britain inhabiting a butterfly hotspot at .70. Consider a random sample of 4 British bird species selected from a total of 10 tagged species. Assume that 7 of the 10 tagged species inhabit a butterfly hotspot. 7 species inhabit a hot spot, 3 do not total number of ways to select 4 species out of 10 is "10 choose 4" 10! / [ 6! * 4! ] = 10 * 9 * 8 * 7 * 6! / [ 6! * 4 * 3 * 2 * 1 ] = 10 * 9 * 8 * 7 / [ 4 * 3 * 2 ] = 210 a. What is the probability that exactly half of the 4 bird species sampled inhabit a butterfly hotspot? number of ways to select 2 from the 7 who inhabit and 2 from 3 who do not = "7 choose 2" * "3 choose 2" = 21 * 3 = 63 probability is 63 / 210 = 3 / 10 b. What is the probability that at least one of the 4 bird species sampled inhabit a butterfly hotspot? do this by reasoning : there are only 3 species who do not, so if we are selecting 4 different species, we will for certain get at least one that does!

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4.77 Suppose you are purchasing cases of wine (12 bottles per case) and that, periodically, you select a test case to determine the adequacy of the bottles' seals. To do this, you randomly select
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## This note was uploaded on 07/29/2010 for the course PH 141 taught by Professor Lahiff during the Summer '10 term at Berkeley.

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hypergeom_solns - sketch of solutions for hypergeometric...

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