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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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A batch contains 36 bacteria cells. Assume that 12 of the

Chapter 2, Problem 224SE

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QUESTION:

Problem 224SE

A batch contains 36 bacteria cells. Assume that 12 of the cells are not capable of cellular replication. Of the cells, 6 are selected at random, without replacement, to be checked for replication.

(a) What is the probability that all 6 of the selected cells are able to replicate?

(b) What is the probability that at least 1 of the selected cells is not capable of replication?

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QUESTION:

Problem 224SE

A batch contains 36 bacteria cells. Assume that 12 of the cells are not capable of cellular replication. Of the cells, 6 are selected at random, without replacement, to be checked for replication.

(a) What is the probability that all 6 of the selected cells are able to replicate?

(b) What is the probability that at least 1 of the selected cells is not capable of replication?

ANSWER:

Solution

Step 1 of 2

Given that no.of bacterial cells in the batch is 36

In that 12 cells are not capable of cellular replication

6 cells are selected without replacement

a) We have to find the probability of all selected 6 cells are able to replicate

No,of cells are able to replicate is 36-12=24

Then the =(24/36)(23/35)(22/34)(21/33)(20/32)(19/31)

                                                            =0.0691

Hence the probability of all selected 6 cells are able to replicate is 0.0691

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