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I don\'t understand if I\'m sampling with or without replacement , so I don\'t k

ID: 3263480 • Letter: I

Question

I don't understand if I'm sampling with or without replacement , so I don't know if I should do nCr or nPr??? how would the answer be different ? thanks

July 17, 2017 STAT 245 Page 1 Statistics 245 Assignment No.3 Instructor: M. Bickis July 17, 2017 Due: 20 July 2017 I. Consider an urn containing black and white balls of which 30% are black. A smple random sample of five balls is taken. Suppose that the urn contains 10 balls. (a) How many possible samples are there? (i.e., how many outcomes are in the sample space?). (b) How many of these samples will contain no black balls? How many will contain exactly one black ball? How many will contain two? Three? Four? Five?

Explanation / Answer

as we do not need to arrange the balls in an order therefore we should use nCr

a) total number of samples =(choosing 5 balls out of 10) =10C5 = 252

b)

as 30% are black ; threfore number of black balls =10*0.3=3

and number of white balls =10-3=7

sample with no black balls =(choosing 5 white balls out of 7) =7C5 =21

samples with 1 black balls =(choosing 4 white balls out of 7 and 1 black ball out of 3) =7C4* 3C1 =35*3=105

samples with 2 black balls =(choosing 3 white balls out of 7 and 2 black ball out of 3) =7C3* 3C2 =35*3=105

samples with 3 black balls =(choosing 2 white balls out of 7 and 3 black ball out of 3) =7C2* 3C3 =21*1=21

as there are only 3 black balls; hence sample with 4 or 5 black balls =0

please revert for any clarification required,

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